ENGINEERING  BIBRAR* 


THE    PROPERTIES    OF 

ELECTRICALLY     CONDUCTING 

SYSTEMS 

Including'  Electrolytes  and   Metals 


BY 
CHARLES  A.  KRAUS 

PROFESSOR    OF    CHEMISTRY   IN    CLARK   UNIVERSITY 


WITH  70  FIGURES  IN  THE  TEXT 


American  Chemical  Society 
Monograph  Series 


BOOK  DEPARTMENT 
The  CHEMICAL  CATALOG  COMPANY,  Inc. 

ONE  MADISON  AVENUE,  NEW  YORK,  U.  S.  A. 
1922 


ENGINEERING  LIBRAHY 


COPYRIGHT,  1922,  BY 

The  CHEMICAL  CATALOG  COMPANY,  Inc. 
All  Rights  Reserved 


Press  of 

J.  J.  Little  &  Ives  Company 
New  York,  U.  S.  A. 


GENERAL   INTRODUCTION 

American    Chemical    Society    Series   /(of 
Scientific    and    Technologic    Monographs 

By  arrangement  with  the  Interallied  Conference  of  Pure  and  Applied 
Chemistry,  which  met  in  London  and  Brussels  in  July,  1919,  the  Ameri- 
can Chemical  Society  was  to  undertake  the  production  and  publication 
of  Scientific  and  Technologic  Monographs  on  chemical  subjects.  At  the 
same  time  it  was  agreed  that  the  National  Research  Council,  in  coopera- 
tion with  the  American  Chemical  Society  and  the  American  Physical 
Society,  should  undertake  the  production  and  publication  of  Critical 
Tables  of  Chemical  and  Physical  Constants.  The  American  Chemical 
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these  two  fields  of  chemical  development.  The  American  Chemical 
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publication  of  the  monographs,  Charles  L.  Parsons,  Secretary  of  the 
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Gellert  Alleman  of  Swarthmore  College.  The  Trustees  have  arranged 
for  the  publication  of  the  American  Chemical  Society  series  of  (a) 
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The  Council,  acting  through  the  Committee  on  National  Policy  of 
the  American  Chemical  Society,  appointed  the  editors,  named  at  the  close 
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are  recognized  as  authorities  in  their  respective  fields.  The  list  of  mono- 
graphs thus  far  secured  appears  in  the  publisher's  own  announcement 
elsewhere  in  this  volume. 

The  development  of  knowledge  in  all  branches  of  science,  and  espe- 
cially in  chemistry,  has  been  so  rapid  during  the  last  fifty  years  and 
the  fields  covered  by  this  development  have  been  so  varied  that  it  is 
difficult  for  any  individual  to  keep  in  touch  with  the  progress  in  branches 
of  science  outside  his  own  specialty.  In  spite  of  the  facilities  for  the 

3 


M542792 


4  GENERAL  INTRODUCTION 

examination  of  the  literature  given  by  Chemical  Abstracts  and  such 
compendia  as  Beilstein's  Handbuch  der  Organischen  Chemie,  Richter's 
Lexikon,  Ostwald's  Lehrbuch  der  Allgemeinen  Chemie,  Abegg's  and 
Gmelin-Kraut's  Handbuch  der  Anorganischen  Chemie  and  the  English 
and  French  Dictionaries  of  Chemistry,  it  often  takes  a  great  deal  of 
time  to  coordinate  the  knowledge  available  upon  a  single  topic.  Con- 
sequently when  men  who  have  spent  years  in  the  study  of  important 
subjects  are  willing  to  coordinate  their  knowledge  and  present  it  in  con- 
cise, readable  form,  they  perform  a  service  of  the  highest  value  to  their 
fellow  chemists. 

It  was  with  a  clear  recognition  of  the  usefulness  of  reviews  of  this 
character  that  a  Committee  of  the  American  Chemical  Society  recom- 
mended the  publication  of  the  two  series  of  monographs  under  the  aus- 
pices of  the  Society. 

Two  rather  distinct  purposes  are  to  be  served  by  these  monographs. 
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activities  may  be  along  a  wholly  different  line.  Many  chemists  fail  to 
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which  on  the  surface  appears  far  afield  from  their  own.  These  mono- 
graphs will  enable  such  men  to  form  closer  contact  with  the  work  of 
chemists  in  other  lines  of  research.  The  second  purpose  is  to  promote 
research  in  the  branch  of  science  covered  by  the  monograph,  by  furnish- 
ing a  well  digested  survey  of  the  progress  already  made  in  that  field  and 
by  pointing  out  directions  in  which  investigation  needs  to  be  extended. 
To  facilitate  the  attainment  of  this  purpose,  it  is  intended  to  include 
extended  references  to  the  literature,  which  will  enable  anyone  interested 
to  follow  up  the  subject  in  more  detail.  If  the  literature  is  so  voluminous 
that  a  complete  bibliography  is  impracticable,  a  critical  selection  will 
be  made  of  those  papers  which  are  most  important. 

The  publication  of  these  books  marks  a  distinct  departure  in  the 
policy  of  the  American  Chemical  Society  inasmuch  as  it  is  a  serious 
attempt  to  found  an  American  chemical  literature  without  primary 
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the  various  organizations  in  the  chemical  and  allied  industries  will  recog- 
nize the  importance  of  the  enterprise  and  take  sufficient  interest  to 
justify  it. 


GENERAL  INTRODUCTION 
AMERICAN    CHEMICAL    SOCIETY 

BOARD   OF  EDITORS 

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Industrial  Hydrogen. 

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Coal  Carbonization. 

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Cyanamide. 

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Wood  Distillation. 

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The  Origin  of  Spectra. 

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Aluminothermic  Reduction  of  Metals. 

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PREFACE 

The  history  of  the  development  of  chemistry  and  molecular  physics 
during  the  past  few  decades  is  largely  an  account  of  the  growth  of  our 
conceptions  of  matter  in  the  ionic  condition.  Whatever  the  shortcomings 
of  the  older  ionic  theory  may  have  been,  it  has  proved  itself  a  powerful 
tool  for  the  purpose  of  disclosing  the  structure  of  material  substances. 
The  intimate  relation  existing  between  matter  and  electricity,  first  in- 
ferred by  Helmholtz  as  a  consequence  of  Faraday's  laws,  has  been  estab- 
lished as  securely  as  the  atomic  theory  itself.  Present  day  conceptions 
as  to  the  nature  of  matter  are,  in  a  large  measure,  the  outgrowth  of 
fundamental  conceptions  underlying  the  ionic  theory.  It  is  true  that 
certain  branches  of  molecular  physics,  to  the  development  of  which  the 
ionic  theory  has  contributed,  have  outstripped  this  theory  in  the  impor- 
tance of  the  results  obtained.  Nevertheless,  the  further  advance  of 
chemistry  is  largely  dependent  upon  the  further  development  of  our  con- 
ceptions of  matter  in  the  ionic  condition. 

A  vast  amount  of  experimental  material  relating  to  this  subject  has 
accumulated  during  the  past  thirty  years.  It  is  found  scattered  through 
the  volumes  of  many  journals  and  the  transactions  of  scientific  societies. 
Unfortunately,  this  material  has  nowhere  been  collected  in  a  form  ren- 
dering it  available  to  those  who  are  not  primarily  interested  in  this  field. 
The  purpose  of  the  present  volume  is  to  present  the  more  important  of 
this  material  in  a  comprehensive  and  systematic  manner,  thus  enabling 
the  reader  to  gain  a  knowledge  of  the  contemporary  state  of  this  subject 
without  an  undue  expenditure  of  time  and  effort.  It  is  hoped,  too,  that 
this  volume  will  prove  useful  to  those  investigators  in  allied  sciences,  who 
find  it  difficult  to  ascertain  the  precise  limitations  underlying  methods 
and  ideas  which  they  often  find  it  necessary  to  apply  in  their  own 
subjects. 

The  systems  treated  are  those  in  which  ionic  phenomena  are  most 
clearly  in  evidence.  Metallic  systems  are  included,  for,  although  the 
nature  of  the  metals  is  but  little  understood,  the  existence  of  a  relation 
between  the  phenomena  in  metallic  and  electrolytic  systems  is  unmis- 
takable. The  treatment  of  metals  is  necessarily  brief,  since  our  knowl- 
edge of  them  is  still  very  uncertain.  The  chemical  aspects  of  metallic 
systems  are,  so  far  as  possible,  kept  in  the  foreground.  A  more  detailed 

7 


8  PREFACE 

treatment  of  the  experimental  material  relating  to  metals  is  unnecessary, 
since  much  of  this  has  already  been  collected  in  various  handbooks. 

Naturally,  the  major  portion  of  this  volume  is  devoted  to  a  con- 
sideration of  the  properties  of  electrolytic  solutions.  The  attempt  has 
been  made  to  present  the  subject  broadly  in  order  to  bring  out  those 
elements  of  the  phenomena  which  are  common  to  solutions  in  all  solvents. 
Solutions  in  non-aqueous  solvents  are  treated  somewhat  more  extensively 
than  aqueous  solutions,  sinc'e  the  data  relating  to  these  solutions  have 
not  been  collected  heretofore. 

The  subject  is  presented  from  an  empirical  standpoint,  since  an  ade- 
quate theory  of  electrolytic  solutions  does  not  exist.  Such  theories  as 
have  been  advanced  in  recent  years  give  evidence  of  having  been  adapted 
to  fit  particular  cases.  In  the  end,  the  theory  of  electrolytic  solutions 
will  probably  be  a  composite  of  various  theories  which  now  appear  more 
or  less  applicable.  Such  a  theory  will  doubtless  embody  some  of  the 
more  fundamental  elements  of  the  older  ionic  theory. 

A  complete  bibliography  has  not  been  attempted.  References  given 
as  footnotes  will  serve  as  a  key  to  the  literature. 

In  conclusion,  I  wish  to  express  my  indebtedness  to  my  colleague, 
Professor  B.  S.  Merigold,  for  reading  the  manuscript  and  to  Mr.  Gordon 
W.  Browne  for  his  assistance  in  preparing  the  figures. 

C.  A.  K. 

Clark  University, 
January  5,  1922. 


CONTENTS 

CHAPTER  PAGE 

I.  INTRODUCTION 13 

1.  Classification  of  Conductors.  2.  Gases.  3.  Metallic 
Conductors.  4.  Electrolytic  Conductors;  a.  Electrolytes 
Which  Conduct  in  the  Pure  State;  b.  Electrolytic  Solutions. 
5.  Electricity  and  Matter.  6.  The  Ionic  Theory. 

II.  ELEMENTARY  THEORY  OF  THE  CONDUCTION  PROCESS  IN  ELEC- 

TROLYTES  19 

1.  Material  Effects  Accompanying  the  Conduction  Process. 
2.  Concentration  Changes  Accompanying  the  Current: 
Hittorfs  Numbers.  3.  The  Conductance  of  Electrolytic 
Solutions.  4.  lonization  of  Electrolytes.  5.  Molecular 
Weight  of  Electrolytes  in  Solution.  6.  Applicability  of  the 
Law  of  Mass  Action  to  Electrolytic  Solutions. 


III.    THE  CONDUCTANCE  OF  ELECTROLYTIC  SOLUTIONS  IN  VARIOUS 

SOLVENTS 46 

1.  Characteristic  Forms  of  the  Conductance-Concentration 
Curve.  2.  Applicability  of  the  Mass-Action  Law  to  Non- 
Aqueous  Solutions.  3.  Comparison  of  the  Ion  Conductances 
in  Different  Solvents. 


IV.  FORM  OF  THE  CONDUCTANCE  FUNCTION 67 

1.  The  Functional  Relation  between  Conductance  and 
Concentration.  2.  Geometrical  Interpretation  of  the  Con- 
ductance Function.  3.  Relation  between  the  Properties  of 
Solvents  and  Their  Ionizing  Power.  4.  The  Form  of  the 
Conductance  Curve  in  Dilute  Aqueous  Solutions.  5.  Solu- 
tions of  Formates  in  Formic  Acid.  6.  The  Behavior  of  Salts 
of  Higher  Type. 

V.  THE  CONDUCTANCE  OF  SOLUTIONS  AS  A  FUNCTION  OF  THEIR 

VISCOSITIES  .     .     ,     .-.'.."; 109 

1.  Relation  between  the  Limiting  Conductance  A0  and  the 
Viscosity  of  the  Solvent.  2.  Change  of  Conductance  as 
Result  of  Viscosity  Change  due  to  the  Electrolyte  Itself.  3. 

9 


10  CONTENTS 

CHAPTER  PAGE 

Relation  between  Viscosity  and  Conductance  on  the  Addition 
of  Non-Electrolytes.  4.  The  Influence  of  Temperature  on 
the  Conductance  of  the  Ions.  5.  The  Influence  of  Pressure 
on  the  Conductance  of  Electrolytic  Solutions. 

VI.  THE  CONDUCTANCE  OF  ELECTROLYTIC  SOLUTIONS  AS  A  FUNC- 

TION OF  TEMPERATURE 144 

1.  Form  of  the  Conductance-Temperature  Curve.  2. 
Conductance  of  Aqueous  Solutions  at  Higher  Temperatures. 
3.  The  Conductance  of  Solutions  in  Non-Aqueous  Solvents 
as  a  Function  of  the  Temperature.  4.  The  Conductance  of 
Solutions  in  the  Neighborhood  of  the  Critical  Point. 

VII.  THE  CONDUCTANCE  OF  ELECTROLYTES  IN  MIXED  SOLVENTS    .     176 

1.  Factors  Governing  the  Conductance  of  Electrolytes  in 
Mixed  Solvents.  2.  Conductance  of  Salt  Solutions  on  the 
Addition  of  Small  Amounts  of  Water.  3.  The  Conductance 
of  the  Acids  in  Mixtures  of  the  Alcohols  and  Water.  4.  Con- 
ductance in  Mixed  Solvents  over  Large  Concentration  Ranges. 


VIII.  NATURE  OF  THE  CARRIERS  IN  ELECTROLYTIC  SOLUTIONS  .     .     198 

1.  Interaction  between  the  Ions  and  Polar  Molecules.  2. 
Hydration  of  the  Ions  in  Aqueous  Solution.  3.  Calculation 
of  Ion  Dimensions  from  Conductance  Data.  4.  The  Hydro- 
gen and  Hydroxyl  Ions.  5.  Ions  of  Abnormally  High  Con- 
ductance. 6.  The  Complex  •  Metal- Ammonia  Salts.  7. 
Positive  Ions  of  Organic  Bases.  8.  Complex  Anions.  9. 
Other  Complex  Ions. 

IX.  HOMOGENEOUS  IONIC  EQUILIBRIA 218 

1.    Equilibria   in   Mixtures   of   Electrolytes.    2.     Hydro- 
lytic  Equilibria. 


X.    HETEROGENEOUS   EQUILIBRIA  IN   WHICH   ELECTROLYTES   ARE 

INVOLVED 232 

1.  The  Apparent  Molecular  Weight  of  Electrolytes  in 
Aqueous  Solution.  2.  The  Molecular  Weight  of  Electrolytes 
in  Non- Aqueous  Solutions.  3.  Solubility  of  Non-Electro- 
lytes in  the  Presence  of  Electrolytes.  4.  Solubility  of  Salts 
in  the  Presence  of  Non-Electrolytes.  5.  Solubility  of  Elec- 
trolytes in  the  Presence  of  Other  Electrolytes ;  a.  Solubility  of 
Weak  Electrolytes  in  the  Presence  of  Strong  Electrolytes  with 
an  Ion  in  Common;  b.  The  Solubility  of  Strong  Binary  Elec- 


CONTENTS  11 

CHAPTER  *AGB 

trolytes  in  the  Presence  of  Other  Strong  Electrolytes;  c.  The 
Solubility  of  Salts  of  Higher  Type  in  the  Presence  of  Other 
Electrolytes. 

XI.  OTHER  PROPERTIES  OF  ELECTROLYTIC  SOLUTIONS      ....     280 

1.  The  Diffusion  of  Electrolytes.  2.  Density  of  Electro- 
lytic Solutions.  3.  Velocity  of  Reactions  as  Affected  by  the 
Presence  of  Ions.  4.  Optical  Properties  of  Electrolytic  Solu- 
tions. 5.  The  Electromotive  Force  of  Concentration  Cells. 
6.  Thermal  Properties  of  Electrolytic  Solutions.  7.  Change 
of  the  Transference  Numbers  at  Low  Concentrations.  8. 
Reactions  in  Electrolytic  Solutions.  9.  Factors  Influencing 
lonization;  a.  The  Ionizing  Power  of  Solvents  in  Relation  to 
Their  Constitution;  b.  The  Relation  between  the  lonization 
Process  and  the  Constitution  of  the  Electrolyte. 

XII.  THEORIES  RELATING  TO  ELECTROLYTIC  SOLUTIONS     .     .     .     323 

1.  Outline  of  the  Problem  Presented  by  Solutions  of  Elec- 
trolytes. 2.  Electrolytic  Solutions  from  the  Thermodynamic 
Point  of  View;  a.  Scope  of  the  Thermodynamic  Method;  b. 
Jahn's  Theory  of  Electrolytic  Solutions;  c.  Comparison  of  the 
Thermodynamic  Properties  of  Electrolytes;  Inconsistencies  in 
the  Older  Ionic  Theory;  The  Thermodynamic  Method; 
Numerical  Values ;  Solubility  Relations  According  to  Bronsted. 
3.  Theories  Taking  into  Account  the  Interionic  Forces;  a. 
Theory  of  Malmstrom  and  Kjellin;  b.  Theory  of  Ghosh;  c. 
Milner's  Theory;  d.  Hertz's  Theory  of  Electrolytic  Conduc- 
tion. 4.  Miscellaneous  Theories.  5.  Recapitulation. 

XIII.  PURE  SUBSTANCES,  FUSED  SALTS,  AND  SOLID  ELECTROLYTES     351 
1.    Substances    Having    a    Low    Conducting    Power.    2. 

Fused  Salts.  3.  Conductance  of  Glasses.  4.  Solid  Elec- 
trolytes. 5.  Lithium  Hydride. 

XIV.  SYSTEMS  INTERMEDIATE  BETWEEN  METALLIC  AND  ELECTRO- 

LYTIC CONDUCTORS 366 

1.  Distinctive  Properties  of  Metallic  and  Electrolytic  Con- 
ductors. 2.  Nature  of  the  Solutions  of  the  Metals  in  Am- 
monia. 3.  Material  Effects  Accompanying  the  Current.  4. 
The  Relative  Speed  of  the  Carriers  in  Metal  Solutions.  5. 
Conductance  of  Metal  Solutions. 

XV.  THE  PROPERTIES  OF  METALLIC  SUBSTANCES      .     .     .     .     .     384 

1.  The  Metallic  State.  2.  The  Conduction  Process  in 
Metals.  3.  The  Conductance  of  Elementary  Metallic  Sub- 


12  CONTENTS 

stances.  4.  The  Conductance  of  Elementary  Metals  as  a 
Function  of  Temperature.  5.  The  Conductance  of  Metallic 
Alloys;  a.  Heterogeneous  Alloys;  b.  Homogeneous  Alloys;  c. 
Solid  Metallic  Compounds;  d.  Liquid  Alloys.  6.  Variable 
Conductors.  7.  The  Conductance  of  Metals  as  Affected  by 
Other  Factors;  a.  Anisotropic  Metallic  Conductors;  b.  Influ- 
ence of  Mechanical  and  Thermal  Treatment;  c.  The  Influence 
of  Pressure  on  Conductance;  d.  Photo-Electric  Properties. 
8.  Relation  between  Thermal  and  Electrical  Conductance  in 
Metals.  9.  Thermoelectric  Phenomena  in  Metals.  10. 
Galvanomagnetic  and  Thermomagnetic  Properties.  11.  Op- 
tical Properties  of  Metals.  12.  Theories  Relating  to  Metallic 
Conduction. 

INDICES  409 


THE  PROPERTIES  OF  ELECTRICALLY 
CONDUCTING  SYSTEMS 

Chapter  I. 
Introduction. 

1.  Classification  of  Conductors.    The  property  of  electrical   con- 
ductance appears  to  be  one  common  to  all  forms  of  matter.    The  value 
of  the  conductance  of  different  forms  of  matter,  however,  varies  within 
very  wide  limits.    Thus,  the  specific  conductance  of  silver  has  a  value 
of  6.0  X  105,  while  that  of  paraffin  is  3.5  X  10~19.     The  specific  con- 
ductance of  gases  under  ordinary  conditions  is  scarcely  measurable.    Nat- 
urally, the  conductance  of  any  given  system  depends  upon  its  state;  and, 
in  general,  any  change  in  the  condition  of  the  system  will  materially 
affect  the  value  of  its  conductance. 

Conductors  may  be  conveniently  grouped  into  a  number  of  classes, 
the  members  of  which  possess  many  properties  in  common. 

2.  Gases.    Under  ordinary  conditions  the  conducting  power  of  gases 
is  of  a  very  low  order,  and  such  conductance  as  they  possess  is  not  an 
intrinsic  property  of  the  gases  themselves,  but  is  due,  rather,  to  the  in- 
fluence of  external  agencies.    Thus,  under  the  action  of  various  radia- 
tions, gases  are  ionized  and  when  in  this  condition  conduct  the  current. 
This  power  of  conduction,  however,  is  lost  when  the  external  source  of 
excitation  is  cut  off.    Whether  or  not  the  gases  themselves  may  possess 
in  some  slight  degree  the  power  of  conducting  the  current  is  uncertain, 
since  the  conducting  power  of  gases  which  have  been  entirely  freed  from 
disturbing  effects  is  of  such  a  low  order  that  the  usual  methods  of  meas- 
urements fail.    The  conductance  of  a  gas  is  a  function  of  its  density. 
It  is  probable  that  at  high  densities  gases  will  exhibit  properties  com- 
parable with  those  of  many  liquids.    In  the  case  of  hexane  it  has  been 
shown  that  the  residual  conductance  on  purification  is  for  the  most  part 
due  to  the  action  of  external  radiations,  which  indicates  that  the  con- 
ductance, which  many  liquid  substances  of  low  conducting  power  possess, 
is  not  a  property  of  the  pure  substances  themselves. 

In  gases,  as  well  as  in  insulating  liquids,  under  the  action  of  external 

13 


14          PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

radiations,  we  have  systems  which  are  not  in  a  state  of  equilibrium. 
These  systems  will  not  be  further  considered  here,  since  they  have  been 
treated  extensively  in  treatises  dealing  with  the  conduction  of  gaseous 
systems.  In  what  follows  we  shall  treat  only  such  systems  as  are  nor- 
mally in  a  conducting  state.  These  may  be  divided  into  two  classes; 
namely,  metallic  and  electrolytic  conductors. 

3.  Metallic  Conductors.    Metallic  conductors  are  characterized  by 
the  absence  of  material  effects  when  a  current  passes  through  a  system 
comprising  one  or  more  conductors  of  this  class  alone.    In  this  respect 
metallic  conductors  are  for  the  most  part  sharply  differentiated  from 
electrolytic  conductors,  in  which  concentration  changes  or  other  material 
effects  accompany  the  passage  of  the  current  through  any  surface  of 
discontinuity.     It  does  not  follow,  however,  that  metallic  and  electro- 
lytic conduction  are  entirely  unrelated  and  that  the  two  processes  of 
conduction  may  not  take  place  more  or  less  simultaneously.     Certain 
substances  apparently  conduct  electrolytically  when  in  one  condition  and 
metallically  when  in  another.    In  other  cases,  a  portion  of  the  current 
appears  to  be  carried  by  a  process  similar  to  that  in  the  metals  and 
another  portion  by  a  process  similar  to  that  in  electrolytes. 

Metallic  conductors  are  also  characterized  by  the  relatively  high 
value  of  their  conducting  power.  While  a  few  metals  exhibit  a  value 
of  the  conductance  comparable  with  that  of  electrolytes,  the  conductance 
of  most  metals  is  many  times  greater  than  that  of  electrolytes.  If  this 
is  true  at  ordinary  temperatures,  it  is  even  more  true  at  lower  tempera- 
tures where  the  resistance  may  ultimately  fall  off  to  practically  zero. 
The  problem  of  metallic  conduction  is  one  possessing  great  interest  and 
one  whose  solution  cannot  but  prove  to  be  of  great  importance  in  the 
development  of  chemistry  and  molecular  physics.  At  the  present  time, 
however,  its  solution  appears  far  from  complete.  While  metallic  con- 
ductors come  within  the  scope  of  the  present  monograph,  it  is  not  in- 
tended to  treat  this  subject  exhaustively. 

4.  Electrolytic  Conductors.    Electrolytic  conductors  are  character- 
ized, in  the  first  place,  by  the  fact  that  the  passage  of  the  current  through 
them  is  accompanied  by  a  transfer  of  matter.    In  a  homogeneous  elec- 
trolytic conductor  this  transfer  of  matter  within  the  body  of  the  con- 
ductor does  not  become  apparent,  but  at  any  point  of  discontinuity 
material  effects  make  their  appearance.     The  material  effects  accom- 
panying the  current  are  subject  to  certain  definite  laws  commonly  known 
as  Faraday's  Laws.     Conductors  for  which  Faraday's  Laws  hold  true 
within  the  limits  of  the  experimental  error  are  termed  electrolytic  con- 
ductors.   We  have  here  to  consider  two  classes  of  electrolytic  conductors: 


INTRODUCTION  15 

First,  those  which  conduct  the  current  when  in  a  pure  state  and,  second, 
those  which  conduct  the  current  as  a  result  of  the  presence  of  other  sub- 
stances. This  latter  class  of  conductors  is  embraced  within  the  term 
electrolytic  solutions. 

a.  Electrolytes  Which  Conduct  in  the  Pure  State.  Within  this  class 
is  included,  in  the  first  place,  the  fused  salts.  With  a  few  exceptions, 
the  fused  salts  are  excellent  conductors  of  the  electric  current.  Their 
specific  conductance  near  the  melting  point  being  of  the  order  of  1.0, 
their  conductance,  therefore,  is  about  1  X  10"5  that  of  silver.  The  salts 
are  compounds  between  a  strongly  electronegative  and  a  strongly  electro- 
positive constituent,  and  it  is  seldom  that  such  substances  do  not  possess 
the  power  of  conducting  the  current  in  a  marked  degree.  As  the  electro- 
positive or  electronegative  nature  of  one  or  the  other  of  the  constituents 
becomes  less  pronounced,  however,  the  conductance  of  the  resulting 
compound  is  diminished.  This  is  the  case,  for  example,  with  mercuric 
chloride. 

When  hydrogen  is  combined  with  a  strongly  electronegative  element 
or  group  of  elements,  the  resulting  compound,  as  a  rule,  exhibits  electro- 
lytic properties.  This,  for  example,  is  the  case  with  water,  which  has 
been  shown  to  conduct  the  current  slightly  when  in  a  pure  state.  At 
18°  its  specific  conductance  has  a  value  of  0.042  X  10~6.  Other  com- 
pounds of  hydrogen  exhibit  similar  properties. 

When  hydrogen  is  combined  with  elements  which  are  less  strongly 
electronegative,  the  resulting  compounds  exhibit  a  lower  conducting 
power.  In  the  case  of  the  hydrocarbons  the  conductance  reaches  ex- 
tremely low  values  and  it  is  possible  that  these  substances  in  the  pure 
state  do  not  possess  the  power  of  conducting  the  current. 

While  substances  in  the  fused  state  are,  as  a  rule,  better  conductors 
than  in  the  solid  state,  electrolytic  conductors  are  not  restricted  to  the 
fused  state,  since  certain  substances  in  the  solid  state  have  been  found 
to  conduct  the  current  quite  as  readily  as  the  fused  salts. 

b.  Electrolytic  Solutions.  The  most  common  electrical  conductors 
are  those  in  which  the  conductance  is  due  to  a  mixture  of  two  or  more 
substances.  As  a  rule,  one  of  these,  the  solvent,  is  present  in  consider- 
able excess  and  may  itself  be  only  a  very  poor  conductor.  In  this  case, 
the  conductance  is  said  to  be  due  to  the  addition  of  the  second  compo- 
nent, termed  the  electrolyte.  To  this  class  belong  all  the  ordinary  solu- 
tions of  salts  in  water.  In  some  cases  an  electrolytic  solution  results 
when  a  substance,  which  itself  in  the  pure  state  is  a  poor  conductor,  is 
added  to  a  second  substance  which  likewise  is  a  poor  conductor  in  the 
pure  state.  As  an  example,  we  may  cite  solutions  of  the  acids  in  water. 


16          PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

Hydrochloric  acid,  for  example,  in  the  pure  state  has  a  conductance  even 
lower  than  that  of  water.  When  dissolved  in  water,  however,  the  con- 
ductance of  hydrochloric  acid  is  much  greater  than  that  of  ordinary  salts 
dissolved  in  the  same  solvent.  This  class  also  includes  solutions  of 
various  organic  oxygen  and  nitrogen  compounds  in  the  liquid  halogen 
acids.  This  behavior,  moreover,  is  not  restricted  to  acids,  since  solu- 
tions of  many  bases,  such  as  ammonia,  result  from  a  mixture  of  two 
components  neither  of  which  possesses  considerable  conductance  in  the 
pure  state.  Where  an  electrolytic  solution  results  from  a  mixture  of  two 
components  which  are  themselves  non-conductors,  it  is  probable  that 
reaction  takes  place  when  the  two  components  are  brought  together,  as 
a  result  of  which  an  electrolyte  is  formed. 

Apparently,  electrolytic  solutions  result  in  all  cases  when  typical 
salts  are  dissolved  in  liquids  up  to  sufficiently  high  concentrations.  The 
property  of  forming  electrolytic  solutions  with  dissolved  salts  is  thus 
not  peculiar  to  water  or  solvents  of  the  water  type,  but  is  a  property 
common  to  all  fluid  media.  It  is  true  that  the  phenomena  are  materially 
altered  as  the  nature  of  the  solvent  medium  changes,  but  otherwise,  if 
the  solutions  are  sufficiently  concentrated,  the  order  of  the  conductance 
values  will  not  differ  greatly  in  different  solvents. 

Among  the  various  properties  of  the  solvent  medium  which  appear 
to  have  a  marked  influence  upon  the  properties  of  the  resulting  electro- 
lytic solution,  the  dielectric  constant  stands  out  as  the  most  important 
factor.  As  the  dielectric  constant  of  the  solvent  medium  decreases,  the 
conductance  of  the  resulting  solutions  is  altered,  but  the  power  to  con- 
duct the  current  is  never  lost,  no  matter  how  low  the  dielectric  constant 
of  the  solvent  medium  may  be.  Thus,  solutions  of  salts  of  organic  bases 
in  chloroform  conduct  fairly  well. 

From  the  standpoint  of  the  development  of  chemistry,  solutions  of 
electrolytes  are  of  first-rate  importance.  Electrolytic  solutions  exhibit  a 
variety  of  phenomena  and  admit  of  a  variety  of  reactions  which  are  not 
to  be  found  in  the  case  of  any  other  system  of  substances.  A  great 
variety  of  reactions  take  place  at  the  electrodes  when  solutions  of  elec- 
trolytes are  electrolyzed,  and,  when  solutions  of  electrolytes  are  mixed, 
reactions  take  place  between  the  constituent  electrolytes.  Reactions  be- 
tween electrolytes  are  characterized  by  the  extreme  facility  with  which 
they  occur.  It  is  only  in  exceptional  cases  that  the  rate  of  such  reac- 
tions is  sufficiently  low  to  admit  of  measurement.  In  solutions  of  elec- 
trolytes, therefore,  we  are  dealing  essentially  with  systems  in  equilibrium. 
This  is  of  importance  in  their  theoretical  treatment,  since  thermodynamic 
principles  may  be  readily  applied  to  systems  in  equilibrium. 


INTRODUCTION  17 

5.  Electricity  and  Matter.    While  electrolytic  solutions  are  thus  of 
great  importance  from  a  practical  point  of  view,  they  have  played  no 
less  important  a  role  in  the  development  of  our  conceptions  of  the  nature 
of  matter  and  the  nature  of  chemical  reactions.    That  electricity  and 
matter  are  intimately  related  was  long  since  pointed  out  by  Helmholtz 
as  a  consequence  of  Faraday's  Law.    Since  in  electrolytes  electricity  and 
matter  are  associated  in  definite  and  fixed  proportions,  and  since  matter 
appears  to  be  discrete  in  its  structure,  it  follows  that  electricity  also  must 
be  discrete  in  its  fundamental  structure.    Corresponding  to  the  atoms, 
the  smallest  subdivisions  of  elementary  substances,  we  have  the  funda- 
mental charge  of  electricity,  the  charge  associated  with  a  single  univa- 
lent  ion,  which  represents  the  smallest  known  subdivision  of  the  electric 
charge.    The  development  of  the  mechanics  of  the  atoms  in  the  last  two 
decades  has  greatly  enlarged  our  knowledge  of  the  fundamental  relation 
between  electricity  and  matter.    The  fundamental  charge  of  electricity, 
the  charge  associated  with  the  negative  electron,  is  objectively  as  real  as 
the  atoms  and  the  molecules  themselves.    The  intimate  relation  of  the 
fundamental  charge  with  the  atoms  or  groups  of  atoms,  which  play  so 
important  a  part  in  many  chemical  reactions,  makes  it  appear  probable 
that  in  chemical  reactions  the  negative  electron  is  primarily  concerned. 
The  horizon  of  chemistry  is  rapidly  broadening  in  this  direction,  and  a 
study  of  electrolytic  systems  will  unquestionably  play  a  great  part  in 
the  ultimate  elucidation  of  the  mechanics  of  chemical  reactions. 

6.  The  Ionic  Theory.    To  account  for  the  various  phenomena  which 
have  been  observed  in  electrolytic  solutions,  the  ionic  theory  has  been 
introduced.     While  ordinarily  the  ionic  theory  is  supposed  to  include 
fundamentally  those  concepts  first  introduced  by  Arrhenius,  this  theory 
is,  in  fact,  a  composite  theory  in  which  many  molecular  mechanical 
hypotheses  are  combined.    It  is  to  Arrhenius  that  is  due  the  credit  of 
first  having  developed  a  theory  of  electrolytes,  quantitative  in  its  nature, 
the  correctness  of  which  it  was  possible  to  determine  by  exact  quantita- 
tive methods.    While  the  gaps  left  in  the  theory  of  electrolytic  solutions 
by  the  work  of  Arrhenius  may  not  be  overlooked,  it  should  not  be  for- 
gotten that  up  to  the  present  time  no  other  theory  has  been  proposed 
which  is  equally  well  able  to  account  for  so  many  and  for  so  large  a 
variety  of  facts. 

The  introduction  of  the  theory  of  Arrhenius  has,  from  the  start,  met 
with  the  most  determined  opposition  on  the  part  of  many  chemists.  It 
is  interesting,  now,  to  note  that  in  recent  years  the  basis  of  the  objections 
to  the  theory  of  Arrhenius  has  greatly  shifted  and  many  of  the  originally 
proposed  objections  have  since  been  found  to  be  without  foundation. 


18          PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

Nevertheless,  the  opposition  to  the  theory  of  Arrhenius  has  continued  to 
find  supporters  even  up  to  the  present  time.  In  part,  at  least,  this  oppo- 
sition has  been  due  to  a  realization  on  the  part  of  chemists  of  the  limi- 
tations of  the  theory  of  which  its  author  has  himself  been  aware.  One 
of  the  fundamental  truths  which  the  theory  of  Arrhenius  has  brought 
to  the  attention  of  chemists  is  the  existence  of  equilibria  in  electrolytic 
systems;  and,  however  the  details  of  his  theory  may  subsequently  be 
modified,  it  would  appear  that  this  most  fundamental  element  of  his 
theory  must  always  be  retained. 


Chapter  II. 

Elementary  Theory  of  the  Conduction  Process  in 
Electrolytes. 

1.  Material  Effects  Accompanying  the  Conduction  Process.  That 
material  effects  accompany  the  passage  of  the  current  through  a  non- 
metallic  medium  was  known  at  an  early  date.  Thus  Nicholson  and 
Carlisle  *  observed  the  decomposition  of  water,  and  Sir  Humphrey  Davy  2 
isolated  the  element  potassium  by  electrolysis  of  the  hydroxide.  While 
it  was  thus  recognized  that  chemical  action  is  intimately  associated  with 
the  passage  of  the  current  through  an  electrolyte,  the  quantitative  rela- 
tionships were  not  studied  until  Faraday  carried  out  his  classical  re- 
searches. It  is  unnecessary  to  give  here  in  detail  the  results  of  Faraday's 
investigations.  It  will  be  sufficient  to  state  the  laws  which  now  bear  his 
name;  namely,  that  chemical  action  accompanying  the  passage  of  the 
current  is  proportional  to  the  quantity  of  electricity  passing,  and  that, 
for  a  given  quantity  of  electricity,  the  chemical  effects  in  the  case  of 
different  reactions  are  equivalent.  These  laws  have  since  been  verified 
by  a  multitude  of  observations  on  the  action  of  the  current  passing 
through  electrolytes.  The  most  exact  measurements  have  been  made 
on  the  deposition  of  silver  and  on  the  liberation  of  iodine.3  In  all  cases, 
Faraday's  Law  has  been  found  to  hold  within  the  limits  of  experimental 
error.  It  has  been  found  to  hold  in  the  case  of  fused  salts  at  higher  tem- 
peratures,4 as  well  as  in  that  of  certain  solid  electrolytes.5 

There  are  cases,  indeed,  where  apparent  exceptions  to  Faraday's  Law 
appear.  For  example,  when  a  current  is  passed  through  a  solution  con- 
taining a  compound  of  sodium  and  lead  in  equilibrium  with  metallic 
lead,  there  are  deposited  on  the  anode  2.25  equivalents  of  lead  per  equiva- 
lent of  electricity.6  Similar  results  have  been  obtained  in  the  case  of 
solutions  of  certain  other  metallic  complexes  in  liquid  ammonia.7  These 
cases,  however,  do  not  constitute  an  exception  to  Faraday's  Law,  since 
there  are  present  in  these  solutions,  presumably,  a  series  of  complexes 

1  Nicholson  and  Carlisle,  Nicholson's  Jour.  4,  179  (1800)  ;  Gilbert's  Ann.  6   340   (1800) 

'Phil.  Trans.  100,  1   (1808). 

1  Bates  and  Vinal,  J.  Am.  Chem.  Soc.  36,  936   (1914). 

*  Richards  and  Stull,  Proc.  Am.  Acad.  S8,  409   (1902). 

"Tubandt  and  Lorenz,  Ztschr.  f.  phys.  Chem.  87,  513   (1914). 

•Smyth,  J.  Am.  Chem.  Soc.  39,  1299  (1917). 

7  Peck,  J.  Am.  Chem.  Soc.  1,0,  335   (1918). 

19 


20          PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

whose  average  composition  corresponds  to  the  reaction  which  occurs  at 
the  electrode  on  electrolysis  of  these  solutions.  The  precipitation  at  the 
anode  in  these  solutions  corresponds  to  the  average  composition  of  the 
complex. 

The  solutions  of  the  alkali  metals  and  the  metals  of  the  alkaline 
earths  in  liquid  ammonia  constitute  another  apparent  exception  to  Fara- 
day's Law,  and  in  order  to  reconcile  the  results  obtained  in  the  case  of 
these  solutions  with  Faraday's  Law  it  is  necessary  to  extend  it.8  When, 
for  example,  a  current  is  passed  through  a  solution  of  sodium  in  liquid 
ammonia,  only  a  fraction  of  the  current  appears  to  be  accompanied  by 
an  observable  material  process.  These  solutions,  therefore,  behave  as 
though  the  current  were  in  part  carried  by  an  electrolytic  and  in  part 
by  a  metallic  process.  In  order  to  reconcile  these  results  with  Faraday's 
Law,  it  is  necessary  to  assume  that  the  process  of  metallic  conduction  is 
likewise  an  ionic  one,  the  current  in  this  case  being  carried  by  the  nega- 
tive electrons.  If  this  hypothesis  is  made,  then  Faraday's  Laws  hold  in 
these  cases  also. 

Faraday's  Laws  lead  to  important  conclusions,  not  only  with  regard 
to  the  mechanism  of  the  conduction  process  in  electrolytes,  but  also  with 
regard  to  the  relation  between  electricity  and  matter.  Interpreted  from 
a  molecular  kinetic  point  of  view,  Faraday's  Laws  state  that  definite  fixed 
quantities  of  electricity  are  associated  with  definite  amounts  of  matter. 
As  Helmholtz 9  pointed  out,  if  matter  consists  of  discrete  particles,  then 
electricity  likewise  is  discrete  in  character.  Corresponding  to  the  atom, 
the  smallest  subdivision  of  matter,  we  have  a  fundamental  electric 
charge,  namely,  the  charge  on  a  univalent  ion.  The  charge,  therefore, 
on  any  given  particle  of  matter,  whether  it  be  of  molecular  or  atomic 
dimensions  or  whether  it  be  of  larger  dimensions  as,  for  example,  a  drop 
of  oil,  may  not  be  varied  continuously  but  only  in  multiples  of  the  unit 
charge.  The  discontinuous  nature  of  the  electric  charge  is  one  of  the 
fundamental  facts  underlying  electrochemical  phenomena  and  must  be 
taken  into  account  in  the  interpretation  of  these  phenomena. 

The  reactions  accompanying  the  passage  of  the  current  through  an 
electrode  surface  indicate  clearly  that  an  intimate  relation  exists  between 
chemical  and  electrical  phenomena.  Berzelius  10  attempted  to  account 
for  the  structure  of  chemical  compounds  by  means  of  an  electrical 
hypothesis.  In  this,  however,  he  was  unsuccessful,  largely  because  he 
assumed  a  false  mechanism  as  representing  the  association  between 
electricity  and  matter.  Instead  of  associating  the  charge  with  the  atoms 

•Kraus,  J.  Am.  Chem.  Soc.  30,  1323   (1908)  ;  36,  864   (1914). 

•Helmholtz,  J.  Chem.  Soc.  39,  277    (1881)  ;  Wiss.  Abh.  3,  p.  52. 

10  Berzelius,  Lehrbuch,  Ed.  3,  Vol.  5   (1835)  ;  Ostwald,  Electrochemie,  p.  335. 


CONDUCTION  PROCESS  IN  ELECTROLYTES  21 

themselves,  in  his  theory,  he  associated  the  charge  with  certain  atomic 
complexes,  which  complexes  in  fact  do  not  exist.  Present  day  concep- 
tions regarding  the  constitution  of  chemical  compounds  do  not  differ  in 
many  respects  from  those  of  Berzelius  save  that  it  is  assumed  that  the 
charge  is  associated  with  the  atoms.  In  recent  years,  as  a  result  of  ex- 
perimental methods  which  have  enabled  us  to  gain  an  insight  into  the 
structure  even  of  the  atoms  themselves,  it  is  becoming  more  and  more 
apparent  that,  in  their  compounds,  the  elements  exist  not  in  an  atomic, 
but  in  an  ionic,  that  is,  in  a  charged,  state.  Under  ordinary  conditions 
this  state  of  the  elements  in  a  compound  is  not  clearly  evidenced,  except 
in  the  case  of  such  compounds  as  are  electrolytes  when  dissolved  in 
suitable  solvents  or  when  in  a  fused  state.  From  the  standpoint  of  chem- 
istry, the  study  of  the  properties  of  electrolytes  is  therefore  not  so  much 
an  end  as  a  means.  In  other  words,  the  study  of  the  properties  of 
electrolytes  constitutes  a  convenient  method  of  acquiring  knowledge 
regarding  the  constitution  of  various  chemical  compounds. 

Faraday  was  not  content  to  merely  state  the  results  of  his  observa- 
tions and  to  combine  these  observations  in  the  form  of  general  laws. 
He  attempted  to  gain  an  insight  into  the  mechanism  of  the  processes 
involved.  It  is  often  assumed  that  the  ionic  theory  dates  from  the 
time  when  Arrhenius  co-ordinated  the  work  of  earlier  investigators  and 
suggested  a  means  for  determining  the  relative  amount  of  carriers  present 
in  an  electrolytic  solution  under  given  conditions.  The  ionic  theory, 
however,  is  much  older  than  this.  Its  foundation  was  laid  by  Faraday,11 
who  recognized  that  in  an  electrolyte  the  current  is  carried  by  positive 
and  negative  electrical  charges  associated  with  definite  material  com- 
plexes moving  in  opposite  directions  through  the  solution.  The  terms 
which  we  now  employ  to  describe  the  phenomena  observed  in  the  pas- 
sage of  the  current  through  an  electrolyte  are  due  to  Faraday,  and  in 
themselves  contain  the  concept  of  motion.  The  chief  contribution  of  the 
later  ionic  theory  consisted  in  devising  methods  which  made  it  possible 
to  determine  the  number  of  carriers  present  in  an  electrolytic  solution. 
Whether  or  not  these  methods,  in  fact,  give  us  a  true  measure  of  the 
number  of  ions  present  under  various  conditions  in  no  wise  affects  the 
correctness  of  the  more  general  conceptions  upon  which  the  ionic  theory 
is  based. 

2.  Concentration  Changes  Accompanying  the  Current:  Hittorf's 
Numbers.  The  concentration  changes  in  the  neighborhood  of  the  elec- 
trodes were  first  investigated  by  Hittorf.12  The  fundamental  conception 

"Faraday,  "Experimental  Researches,"  Vol.  1. 
"Hittorf,  Pogg.  Ann.  89,  177   (1853). 


22          PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

underlying  these  concentration  changes  is  that,  within  the  solution,  the 
electric  current  is  carried  by  positive  and  negative  carriers  which  move 
with  velocities  proportional  to  the  potential  gradient  existing  in  the 
solution.  Within  the  body  of  the  electrolyte  itself,  Ohm's  law  is  obeyed. 
The  observed  concentration  change  at  an  electrode  is  thus  the  resultant 
of  two  effects;  namely,  loss  or  gain  due  to  the  reaction  at  the  electrode 
and  loss  or  gain  due  to  the  motion  of  the  positively  and  negatively 
charged  carriers.  The  simplest  case  is  that  in  which  precipitation  of 
the  ions  takes  place  at  the  electrodes.  Let  us  assume  that  the  charge  u 
is  transported  through  the  solution  by  the  cation  and  the  charge  v  by 

the  anion.    Then  — — —  will  be  the  fraction  of  the  charge  carried  by  the 

positive  ion  and  — -p—  the  fraction  of  the  charge  carried  by  the  negative 

ion.  If  one  equivalent  of  material  is  precipitated  at  the  cathode,  then 
u  and  v  will  represent  the  number  of  equivalents  of  matter  carried  up 
to  the  electrodes  as  cation  and  anion  respectively.  The  concentration 
change  in  the  neighborhood  of  the  cathode  will  correspond  to  a  loss  of 
one  equivalent  of  the  electrolyte  due  to  precipitation  at  the  electrode  and 

to  a  gain  of  — -:-—  equivalents  carried  up  to  the  electrode  by  the  cations. 
The  total  observed  concentration  change,  therefore,  will  be  equal  to  the 
difference  of  these  two  or  to  a  loss  of  — -r— -  equivalents.  Similarly, 

at  the  anode,  the  change  will  correspond  to  equivalents.     It  is 

evident  that,  if  the  concentration  change  due  to  the  passage  of  a  given 
charge  is  known  and  if  the  nature  of  the  electrode  reactions  is  known, 

?  J  ?/ 

then  the  ratios  — — —  and  — — —  may  be  determined.     These  ratios, 

which  Hittorf  termed  the  "transference  numbers"  of  the  cation  and  anion, 
respectively,  we  shall  denote  by  the  symbols  n  and  1  —  n. 

In  determining  the  transference  numbers  of  an  electrolyte  by  the 
method  of  Hittorf,  the  concentration  changes  are  measured  with  respect 
to  water.  In  other  words,  the  determination  of  these  numbers  is  based 
upon  the  assumption  that  water  itself  remains  at  rest,  and  is  in  no  wise 
concerned  in  the  process  of  the  transfer  of  electricity  through  the  solution. 
We  now  know  that  this  condition  is  not  strictly  fulfilled  and  that  water 
plays  a  part  in  the  conduction  process.  When  a  current  of  electricity 
passes  through  an  aqueous  solution,  the  solvent  itself  is  transferred  to 
some  extent  along  with  the  ions.  Obviously,  this  will  affect  the  concen- 


CONDUCTION  PROCESS  IN  ELECTROLYTES  23 

tration  changes  observed  at  the  electrodes.  In  order  to  determine  the 
relative  amounts  of  solvent  transferred  by  the  two  ions,  it  is  necessary 
that  there  should  be  present  in  the  solution  some  reference  substance 
which  remains  at  rest  when  the  current  passes  through  the  solution.  The 
concentration  changes  may  then  be  referred  to  this  reference  substance 
and  the  true  transference  numbers  of  the  electrolyte  determined,  together 
with  the  relative  amounts  of  water  associated  with  the  transfer  of  the 
charge  through  the  solution.  Since  the  results  of  such  measurements  will 
be  discussed  in  detail  in  another  chapter,  it  will  be  unnecessary  to  proceed 
further  with  their  discussion  here.  They  have  been  alluded  to  at  this 
point  merely  for  the  purpose  of  calling  attention  to  the  fundamental 
assumption  underlying  the  Hittorf  method  of  determining  transference 
numbers. 

That  the  passage  of  the  current  through  an  electrolyte  is  accompa- 
nied by  a  transfer  of  matter  may  also  be  shown  by  other  means,  as,  for 
example,  by  introducing  a  surface  of  discontinuity  13  in  the  path  of  a 
conducting  electrolyte.  Such  surfaces  of  discontinuity  may  be  observed 
visually  and  thus  yield  a  very  direct  method  for  demonstrating  the  trans- 
fer of  matter  by  means  of  the  current  within  the  body  of  the  electrolyte. 
If,  for  example,  a  solution  containing  hydrochloric  acid  is  superimposed 
on  a  solution  containing  potassium  chloride  and  a  current  is  passed 
through  the  boundary  of  these  solutions  in  such  direction  that  the  more 
rapidly  moving  ion,  namely,  in  this  case,  the  hydrogen  ion,  precedes 
the  more  slowly  moving  ion,  the  potassium  ion,  then  the  boundary  be- 
tween the  two  solutions  will  advance  in  the  direction  of  the  positive 
current.  The  rate  of  motion  of  the  boundary  under  a  given  potential 
gradient  will  depend  upon  the  speed  of  the  carriers.  If  a  solution  of  an 
electrolyte  is  placed  between  solutions  of  two  other  electrolytes,  each  of 
which  has  one  ion  in  common  with  the  first,  then,  under  the  action  of  a 
potential,  the  two  boundaries  will  move  in  opposite  directions,  the  boun- 
dary between  the  cations  moving  toward  the  cathode  and  that  Between 
the  anions  toward  the  anode.  It  is  of  course  necessary  that  the  condi- 
tions for  stability  of  the  boundaries  should  be  fulfilled.  This  requires 
that  at  each  boundary  the  more  rapidly  moving  ion  shall  move  in  ad- 
vance of  the  more  slowly  moving  ion.  Allowing  for  certain  corrections 
which  must  be  made,  the  ratio  of  the  speeds  of  the  two  boundaries  is 
proportional  to  the  current  carrying  capacities  of  the  two  ions.14 

While  the  method  of  moving  boundaries  may  thus  be  employed  for 
measuring  the  transference  numbers  of  electrolytes,  its  chief  value,  per- 

u  Lodge,  Brit.  Ass.  Reports,  p.  389   (1886). 
"Lewis,  J.  Am.  Chem.  Soc.  32,  863  (1910). 


24         PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

haps,  lies  in  that  it  enables  us  to  observe  the  motion  of  the  electrolyte 
within  the  solution  visually. 

The  results  of  transference  measurements  cannot  be  interpreted  with- 
out a  knowledge  of  the  nature  of  the  ions  within  the  solution.  The 
transference  numbers  are  calculated  from  the  observed  concentration 
changes  on  an  assumption  as  to  the  nature  of  the  ions  themselves.  For 
example,  in  determining  the  transference  numbers  of  potassium  chloride 
by  the  Hittorf  method,  it  is  assumed  that  only  potassium  is  transferred 
to  the  cathode  and  chlorine  to  the  anode.  If,  however,  ions  different  from 
those  assumed  exist  in  the  solution,  these  will  take  part  in  the  transfer 
of  electricity  and  will  have  an  influence  upon  the  observed  concentration 
changes  at  the  electrodes.  The  question  as  to  whether  or  not  the  ions 
have  the  simple  structure  commonly  assumed  is  one  which  ultimately 
must  be  answered  on  the  basis  of  considerations  derived  from  other  prop- 
erties of  these  solutions.  That  complex  ions  are  formed  in  the  case  of 
certain  solutions  was  conclusively  shown  by  Hittorf.15  He  found  that 
in  solutions  of  cadmium  iodide  the  transference  number  of  the  cation, 
as  measured,  is  greater  than  unity.  Since  this  ion  cannot  transport 
more  current  than  the  total  passing  through  the  solution,  it  is  obvious,  as 
Hittorf  pointed  out,  that  the  result  may  be  accounted  for  by  assuming 
that  complex  cations  are  formed  by  means  of  which  iodine  is  transferred 
from  the  anode  to  the  cathode.  The  effect  of  this  is  to  lessen  the  con- 
centration increase  of  iodine  in  the  neighborhood  of  the  anode  due  to 
the  transfer  of  the  iodide  ion. 

If  either  positive  or  negative  ions  of  more  than  one  kind  occur  in 
solution,  an  equilibrium  must  exist  among  them  by  virtue  of  which  the 
relative  concentration  of  these  ions  will  be  a  function  of  the  total  con- 
centration of  the  salt.  In  general,  with  decrease  in  concentration,  the 
more  complex  ions  break  up  into  simpler  ones.  It  follows,  therefore, 
that  if  complex  ions  exist  in  solution,  the  transference  numbers  should 
vary  as  a  function  of  the  concentration. 

We  may  now  examine  the  numerical  values  of  the  transference  num- 
bers which  have  been  determined  for  various  electrolytes  and  which  are 
given  in  Table  I.16  At  a  concentration  of  5  millimols  per  liter,  the  cation 
transference  number  for  sodium  chloride,  for  example,  is  0.396.  Corre- 
spondingly, the  anion  transference  number  is  0.604.  This  means  that  in 
a  sodium  chloride  solution  of  this  concentration  the  fraction  0.396  of 
the  current  is  carried  by  positively  charged  carriers,  and  the  remainder 
by  negatively  charged  carriers.  It  will  be  observed  that,  in  general,  the 

"Hittorf,  loc.  cit. 

"Noyes  and  Falk,  J.  Am.  Chem.  Soc.  S3,  1436  (1911). 


CONDUCTION  PROCESS  IN  ELECTROLYTES 
TABLE  I. 


25 


CATION  TRANSFERENCE  NUMBERS  (X  103)  OF  VARIOUS  ELECTROLYTES  IN 
WATER  AT  OR  NEAR  18°. 


Electrolyte          Temp. 


Concentration 
0.0050.01    0.02   0.05     0.1     0.2     0.3     0.5 


1.0 


NaCl  

...  18° 

396 

396 

396 

395 

393 

390 

388 

382 

369 

Kri 

18 

496 

496 

496 

496 

495 

494 

LiCl  

...18 

332 

328 

320 

313 

304 

299 

NH  Cl 

18 

492 

492 

492 

NaBr 

18 

395 

395 

395 

KBr 

18 

495 

495 

A  (/NO 

18 

471 

471 

471 

471 

HC1  

...18 

832 

833 

833 

834 

835 

837 

838 

840 

844 

HNO 

20 

839 

840 

841 

844 

BaCl 

16 

420 

408 

401 

391 

CaCl 

..  20 

440 

432 

424 

413 

404 

395 

389 

SrCl 

20 

441 

435 

427 

CdCl 

18 

430 

430 

430 

430 

430 

CdBr, 

...18 

430 

430 

430 

430 

429 

410 

389 

350 

222 

OdL 

...18 

445 

444 

44?, 

396 

296 

127 

46 

3 

Na  SO 

18 

392 

390 

383 

K  SO 

18 

494 

492 

490 

Tl  SO 

25 

478 

476 

H2S04 

...20 

822 

822 

822 

820 

818 

816 

812 

Ba(N(X), 

..  .  25 

456 

456 

456 

Pb(NO  ) 

25 

487 

487 

MeSO. 

...18 

388 

385 

381 

373 

CdS04  

...18 

389 

384 

374 

364 

350 

340 

323 

294 

CuSO, 

,  18 

375 

375 

373 

361 

348 

327 

transference  numbers  are  functions  of  the  concentration.  This  concen- 
tration effect  is  much  more  pronounced  in  concentrated  than  in  dilute 
solutions,  where  these  numbers  appear  to  approach  limiting  values.  If 
the  underlying  assumptions  are  correct  and  if  complex  ions  are  not 
present  in  solutions  of  these  electrolytes,  then  the  change  in  the  trans- 
ference numbers  at  higher  concentrations  indicates  a  change  in  the  rela- 
tive speed  of  these  ions.  In  general,  at  higher  concentrations  the  trans- 
ference number  of  the  more  slowly  moving  ion  decreases.  A  portion  of 
the  effect  at  higher  concentrations  may  be  due  to  a  transfer  of  water 
with  the  ions.  But  this  is  not  sufficient  to  account  for  the  entire  change 
in  the  transference  numbers.  In  most  cases,  the  change  in  the  transfer- 
ence numbers  does  not  become  pronounced  until  concentrations  are 
reached  where  the  viscosity  of  the  solution  is  materially  affected  by  the 
electrolyte.  Since  the  motion  of  a  particle  through  a  viscous  medium 


26          PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

is  a  function  of  its  viscosity,  it  may  be  inferred  that  in  part,  at  least, 
the  variation  in  the  transference  numbers  at  the  higher  concentrations 
is  due  to  the  change  of  the  viscosity  of  the  solution. 

It  will  be  observed  that  the  transference  numbers  for  potassium 
chloride  are  very  nearly  0.5.  In  other  words,  in  the  case  of  this  salt, 
each  ion  carries  very  nearly  one  half  of  the  current.  If  the  frictional 
resistance,  which  an  ion  meets  in  its  motion  through  the  medium,  is  inde- 
pendent of  the  sign  of  its  charge,  then  this  indicates  that  the  two  ions 
have  approximately  the  same  dimensions.  This  is  borne  out  by  the 
measurements  of  Washburn  16tt  who  showed  that  these  ions  are  hydrated 
to  approximately  the  same  extent. 

The  transference  numbers  of  electrolytes  are  functions  of  the  tem- 
perature. In  Table  II 17  are  given  the  transference  numbers  of  a  number 

TABLE  II. 

CATION  TRANSFERENCE  NUMBERS  (X  10:l)  OF  VARIOUS  ELECTROLYTES  AS 
FUNCTIONS  OF  THE  TEMPERATURE. 

Temp.          NaCl          KC1  HC1  BaCl2 

0°  387  493  845  437 

10  ...  495  841  441 

18  397  496  833 

30  404  498  823  444 

50  ...  ...  801  475 

96  ...  ...  748 

of  electrolytes  at  temperatures  from  0°  to  96°  at  concentrations  in  the 
neighborhood  of  0.015  N.  In  the  case  of  potassium  chloride,  the  trans- 
ference number  varies  only  very  little  with  the  temperature,  whereas  in 
that  of  sodium  chloride  the  transference  number  of  the  cation  increases, 
and  in  that  of  hydrochloric  acid  it  decreases.  As  we  shall  see  later,  it  is 
a  general  rule  that  with  increase  of  temperature  the  transference  numbers 
of  all  electrolytes  approach  the  value  0.5.  The  transference  numbers  of 
ions  having  values  greater  than  0.5,  therefore,  decrease  with  increasing 
temperature;  and  those  having  smaller  values  increase  under  the  same 
conditions. 

3.  The  Conductance  of  Electrolytic  Solutions.  The  conductance  of 
an  electrolytic  solution  is  a  function  of  the  various  factors  which  deter- 
mine its  condition,  such  as  concentration,  temperature,  etc.  The  quan- 
tity actually  measured  is  the  specific  conductance  of  the  solution.  This 
is  defined  as  the  conductance  in  reciprocal  ohms  of  a  column  of  electro- 

"*  Washburn,  J.  Am.  Chem.  800.  31,  322   (1909). 
17  Noyes  and  Falk,  loc.  cit. 


CONDUCTION  PROCESS  IN  ELECTROLYTES  27 

lyte  having  a  cross-section  of  1  sq.  cm.  and  a  length  of  1  cm.  The  spe- 
cific conductance  is  a  function  of  concentration,  increasing,  in  general, 
with  increasing  concentration.  However,  in  the  case  of  certain  electro- 
lytes at  very  high  concentrations,  the  specific  conductance  passes  through 
a  maximum.  This  is  the  case,  for  example,  with  sulphuric  and  hydro- 
chloric acids  dissolved  in  water,  as  well  as  with  certain  other  electro- 
lytic solutions. 

The  specific  conductance,  however,  is  a  quantity  which  is  not  well 
adapted  to  the  purpose  of  comparing  the  conductance  of  different  electro- 
lytes. In  the  case  of  this  property,  as  in  that  of  many  others,  it  is  ad- 
vantageous to  refer  the  numerical  values  to  equivalent  amounts  of  the 
dissolved  electrolyte.  If,  therefore,  the  conductance  of  a  given  electro- 
lyte at  two  given  concentrations  is  to  be  compared,  the  specific  con- 
ductance is  divided  by  the  equivalent  concentration.  This  quantity  is 
called  the  equivalent  conductance.  As  stated  above,  the  specific  con- 
ductance is  referred  to  a  unit  cube  of  the  electrolyte;  that  is,  to  a  cube 
having  a  length  of  1  cm.  and  a  cross-section  of  1  sq.  cm.  In  order  to 
avoid  unnecessary  factors  in  the  expression  for  the  equivalent  con- 
ductance, it  is  desirable  to  express  the  concentration  of  the  electrolyte 
in  equivalents  per  cubic  centimeter,  rather  than  in  equivalents  per  liter.18 
In  what  follows  we  shall  employ  the  Greek  letter  j\  to  express  the  con- 
centration in  equivalents  per  c.c.,  while  the  letter  C  will  be  employed  to 
express  the  concentration  in  equivalents  per  liter.  We  have  therefore 
lOOOi]  =  C.  If  we  represent  the  equivalent  conductance  by  the  Greek 
letter  A,  and  the  specific  conductance  by  the  Greek  letter  \L,  then  we 
obviously  have: 

»>       :    *-$ 

The  value  of  the  equivalent  conductance  A  measures,  in  fact,  the 
conducting  power  of  the  electrolyte  in  a  solution  of  a  given  concentra- 
tion. Suppose,  for  example,  that  one  equivalent  of  electrolyte  were  con- 
tained between  two  electrodes  1  cm.  wide,  separated  by  1  cm.,  and  of 
indefinite  extent  vertically.  If  the  entire  electrolyte  were  contained  in 
1  cu.  cm.  of  liquid,  then  the  equivalent  conductance  would  obviously  be 
equal  to  the  specific  conductance  at  this  concentration,  which  is  unity. 
If,  now,  more  solvent  were  added  to  this  solution,  the  amount  of  solute 
remaining  constant,  the  concentration  of  the  solution  would  be  decreased. 
At  the  same  time  there  would  be  an  increase  in  the  electrode  area,  but 
the  total  amount  of  conducting  material  between  the  electrodes  and  the 

»  Kohlrausch  and  Holborn,  "Leitvermogen  der  Elektrolyte,"  1898,  p.  84. 


28 


PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 


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CONDUCTION  PROCESS  IN  ELECTROLYTES 

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29 


30         PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

average  distance  which  the  conducting  particles  would  have  to  travel 
between  these  electrodes  would  remain  fixed.  If  the  cell  were  filled  to  a 
height  of  I  centimeters  and  if  the  conductance  of  the  solution  between 
the  pair  of  electrodes  were  A,  then,  since  the  electrode  area  is  equal  to 
the  reciprocal  of  the  concentration,  i.e.,  to  I/  1,  it  follows  that  the  specific 
conductance  of  this  solution  would  be: 


Therefore,  in  order  to  compare  the  conducting  power  of  a  solution  of  a 
given  electrolyte  at  different  concentrations,  we  divide  the  specific  con- 
ductance of  the  solution  by  the  concentration  and  compare  the  values 
of  this  ratio,  namely  the  values  of  A.  Similarly,  in  comparing  the  con- 
ducting power  of  solutions  of  different  electrolytes  in  the  same  or  different 
solvents  at  the  same  concentration,  the  values  of  the  equivalent  con- 
ductance of  the  electrolytes  at  that  concentration  are  obviously  to  be 
compared.  The  equivalent  conductance  is  a  measure  of  the  conducting 
of  an  equivalent  amount  of  material.  In  comparing  the  conducting 
power  of  solutions,  therefore,  we  require  the  values  of  the  equivalent 
conductance  A  for  these  solutions. 

Values  of  the  equivalent  conductance  of  typical  electrolytes  in  water 
at  18°  are  given  in  Table  III.19  The  concentrations  in  this  case  are  ex- 
pressed in  equivalents  per  liter.  It  will  be  observed  that  as  the  concen- 
tration of  an  electrolyte  in  water  decreases,  its  equivalent  conductance 
increases.  For  a  decrease  in  the  concentration  in  the  ratio  of  one  to  two 
between  normal  and  half  normal,  the  equivalent  conductance  of  a  binary 
electrolyte  increases  approximately  30%.  For  a  corresponding  decrease 
in  concentration  between  1  and  0.5  milli-equivalent  per  liter,  the  equiva- 
lent conductance  increases  less  than  1%.  It  is  apparent,  therefore,  that 
as  the  concentration  decreases,  the  equivalent  conductance  approaches  a 
limiting  value. 

The  relation  between  the  equivalent  conductance  and  the  concentra- 
tion is  shown  graphically  in  Figure  1,  where  values  of  the  equivalent 
conductance  of  aqueous  solutions  of  KC1,  NaCl  and  LiI03  are  plotted 
as  ordinates  and  the  logarithms  of  the  concentrations  as  abscissas.  The 
curves  for  different  electrolytes  are  evidently  similar  in  form.  As  the 
concentration  decreases,  the  equivalent  conductance  apparently  ap- 
proaches a  definite  value  as  a  limit.  A  curve  of  this  type,  however,  does 
not  lend  itself  to  a  determination  of  the  limiting  value  which  the  con- 
ductance approaches  as  the  concentration  'decreases  indefinitely.  For 

19Noyes  and  Falk,  J.  Am.  Client.  Soc.  3^,  454  (1912). 


CONDUCTION  PROCESS  IN  ELECTROLYTES 


31 


the  purposes  of  graphical  extrapolation  it  is  preferable  to  employ  some 
function  of  the  concentration  which  brings  the  point  of  zero  concentra- 
tion, to  which  the  extrapolation  must  be  carried,  to  one  of  the  axes  on  the 
plot.  A  convenient  function  which  yields  a  simple  type  of  curve  is  the 
cube  root  of  the  concentration.  Such  plots  for  potassium  chloride  and 
sodium  chloride  are  shown  in  Figure  2.  If  the  curves  for  potassium 
chloride  and  sodium  chloride  are  extrapolated,  they  yield  for  the  limit- 
ing value  of  the  equivalent  conductance  values  in  the  neighborhood  of 
130.0  and  108.9  respectively.  The  value  obtained  for  A0  will,  of  course, 
depend  upon  the  extrapolation  function  employed.  In  another  chapter 


I 


140 


\zo 


100 


60 


40 


20 


£S  4.0  4S  AO          3*  ?.0         ZJS  T.O  f.5  0.0 

Log  C. 

FIG.  1.    Showing  A  as  a  Function  of  Log  C  for  Aqueous  Solutions  at  18°. 

various  functions  proposed  for  this  purpose  will  be  discussed  more  in 
detail.  For  the  present  it  will  be  sufficient  to  employ  approximate  values 
for  the  purpose  of  comparing  the  behavior  of  different  electrolytes. 

The  equivalent  conductance  of  hydrochloric  acid  is  much  greater  than 
that  of  the  salts.  The  conductance  curve,  however,  is  similar  in  form 
to  that  of  the  salts.  That  is,  with  decreasing  concentration,  the  equiva- 
lent conductance  approaches  a  limiting  value.  In  the  case  of  hydro- 
chloric acid  this  value  is  in  the  neighborhood  of  380  at  18°.  We  may 
now  ask  the  question:  To  what  are  the  differences  in  the  values  of  the 
equivalent  conductance  of  the  different  electrolytes  due?  Why,  for  ex- 
ample, is  the  equivalent  conductance  of  hydrochloric  acid  greater  than 
that  of  potassium  chloride?  Or,  in  other  words,  to  what  is  the  greater 


32 


PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 


conductance  of  hydrochloric  acid  due?  It  will  be  recalled  that  at  a 
temperature  of  18°  and  a  concentration  of  0.01  normal,  for  example,  the 
value  of  the  transference  numbers  of  the  positive  ions  in  sodium  chlo- 
ride, potassium  chloride  and  hydrochloric  acid  are  0.396,  0.496  and 
0.833  respectively.  In  the  case  of  these  electrolytes  the  negative  carrier 


Equivalent  Conductance  A. 

*  8  g  5  |  g 

X 

x 

\. 

X 

\ 

x 

\«, 

\ 

70 

x 

o.o         as          0.4          o.e           o.&          1. 

Cube  Root  of  Concentration,  C%. 
FIG.  2.    Showing  A  as  a  Function  of  C^. 

is  presumably  the  same,  namely,  the  chloride  ion,  and  it  is  only  the  posi- 
tive carriers  which  differ  in  these  electrolytes.  If,  then,  the  negative 
carriers  are  the  same  in  solutions  of  these  electrolytes,  it  may  be  assumed 
that  the  current  carried  by  these  carriers  in  these  solutions  under  the 
same  conditions  of  temperature  and  concentration  will  be  approximately 
the  same,  and  consequently  the  difference  in  the  conducting  power  of 
these  electrolytes  is  due  to  the  difference  in  the  conducting  power  of 
their  positive  carriers.  The  carrying  capacities  of  the  spdium,  potassium 


CONDUCTION  PROCESS  IN  ELECTROLYTES  33 

and  the  hydrogen  ions  are,  therefore,  0.656,  0.984  and  1.972  times  that 
of  the  chloride  ion  respectively.  In  other  words,  the  carrying  capacity 
of  the  hydrogen  ion  is  3  times  that  of  the  sodium  ion  and  2  times  that 
of  the  potassium  ion.  If  the  tables  of  the  conductance  and  of  the  trans- 
ference numbers  are  compared,  it  will  be  seen  that  in  the  more  dilute 
solutions  it  is  generally  true  that,  for  salts  having  an  ion  in  common, 
those  salts  whose  ions  have  greater  transference  numbers  likewise  have 
greater  conducting  power. 

We  now  come  to  an  important  generalization  due  to  Kohlrausch,20 
namely:  In  a  solution  of  a  single  electrolyte,  the  two  ions  move  inde- 
pendently of  each  other.  Therefore,  we  may  determine  the  fraction  of  the 
current  carried  by  each  ion,  or,  in  other  words,  the  conductance  of  each 
ion  in  a  given  solution,  by  multiplying  the  equivalent  conductance  of 
the  solution  by  the  transference  number  of  the  electrolyte  in  this  solu- 
tion. If  this  is  true,  then,  in  a  solution  of  sodium  chloride  having  a 
concentration  of  0.01  normal  at  18°,  the  conductance  due  to  the  sodium 
ion  is  101.88  X  0.396  =rANa=  40.34.  Similarly,  the  conductance  of  the 

potassium  and  hydrogen  ions  under  the  same  conditions  is: 

AK  =  122.37  X  0.496  =  60.69 
and  AH  =  369.3    X  0.833  =  307.63 

In  these  solutions  the  conductance  of  the  chloride  ion  is  61.54,  61.68  and 
61.67  for  NaCl,  KC1  and  HC1  respectively.  The  conductance  of  the 
chloride  ion  is  thus  very  nearly  the  same  in  equivalent  solutions  of  these 
electrolytes.  It  is,  however,  by  no  means  certain  that  the  conductance 
of  a  given  ion  will  in  all  cases  be  the  same  in  solutions  of  different  salts. 
If  the  transference  numbers  of  an  electrolyte  are  known  at  a  given  con- 
centration, then  the  conductance  of  its  ions  may  be  calculated. 

4.  lonization  of  Electrolytes.  As  we  have  seen,  the  equivalent  con- 
ductance of  a  solution,  which  measures,  so  to  speak,  the  conducting 
power  of  the  dissolved  electrolyte  under  given  conditions,  increases  with 
decreasing  concentration  and  appears  to  approach  a  limiting  value.  The 
current  passing  through  an  electrolyte  under  given  conditions  is  carried, 
in  the  case  of  the  simpler  types  of  salts,  by  two  charged  constituents, 
namely  the  positive  and  the  negative  carriers,  which,  according  to  Fara- 
day, are  termed  the  cation  and  the  anion  respectively.  The  relative 
amounts  of  the  current  carried  by  the  positive  and  negative  ions  may 
be  determined  by  means  of  transference  experiments,  which  depend  ulti- 
mately upon  the  concentration  changes  produced  by  the  motion  of  the 

"Gottinger,  "Nachrichten,"  1876,  p.  213. 


34      PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

carriers.  If  the  current  in  a  solution  of  an  electrolyte  is  effected  through 
the  motion  of  charged  carriers  within  the  electrolyte,  then  we  may  in- 
quire: What  fraction  of  the  electrolyte  present  in  the  solution  is  con- 
cerned in  the  process  of  conduction;  that  is,  what  fraction  of  the  electro- 
lyte exists  in  an  ionic  condition? 

Clausius  21  suggested  that  electrolytes  are  ionized,  but  he  failed  to 
draw  any  definite  conclusion  as  to  the  extent  of  this  ionization.  In  his 
time,  the  notion  that  a  stable  compound,  such  as  potassium  chloride, 
could  be  dissociated  and  moreover  dissociated  into  oppositely  charged 
constituents  was  contrary  to  accepted  theories.  Clausius  was  therefore 
content  to  merely  throw  out  the  suggestion  that  electrolytes  are  to  some 
extent  dissociated. 

The  conclusion  that  an  electrolyte  is  dissociated  follows  almost  neces- 
sarily from  the  work  of  Kohlrausch  and  Hittorf,  although  neither  of 
these  investigators  actually  drew  this  conclusion.  It  was  Arrhenius22 
who  proposed  the  fundamental  hypothesis  that  an  electrolyte  in  solution 
is  dissociated  and  that  the  degree  of  its  dissociation  may  be  determined 
by  means  of  the  conductance  of  its  solutions.  Moreover,  he  showed  that 
the  dissociation  as  measured  in  this  way  is  in  agreement  with  many 
other  well-known  properties  of  these  solutions. 

We  have  seen  that,  as  the  concentration  of  a  solution  decreases,  its 
equivalent  conductance  increases  and  approaches  a  limiting  value.  We 
have  also  seen  that  the  positive  and  negative  ions  within  the  electrolyte 
appear  to  move  at  definite  rates  under  fixed  conditions,  provided  the  con- 
centration of  the  solution  is  not  too  great,  and  that  the  motion  of  the 
ions  under  these  conditions  takes  place  independently  for  each  ion.  If 
these  conclusions  are  correct,  then  it  appears  that  a  logical  explanation  of 
the  facts  would  be  that,  in  the  more  concentrated  solutions,  a  portion  of 
the  electrolyte  has  been  removed  from  a  condition  in  which  it  is  able 
to  take  part  in  the  conduction  process,  while  the  fraction  of  the  sub- 
stance which  remains  in  a  conducting  condition  is  measured  by  the  ratio 
of  the  conductance  at  a  given  concentration  to  the  conductance  at  very 
low  concentrations,  where  apparently  all  the  electrolyte  takes  part  in  the 
conduction  process. 

Let  y  represent  the  fraction  of  the  salt  present  in  a  conducting  state; 
then  the  relative  amount  of  the  salt  present  in  this  state  at  any  con- 
centration will  be  given  by  the  ratio: 


"Clausius,  Pogg.  Ann.  101,  338   (1857). 

»  Arrhenius,  Bijlumj  till  K.  Svenska,  Vet.  Akad.  Handl.  No.  13,  1884;  Sixth  Circular 
of  the  British  Association  Committee  for  Electrolysis,  May,  1887  ;  Zfschr.  f.  nhys.  Cfiem.. 
1,  631  (J887), 


CONDUCTION  PROCESS  IN  ELECTROLYTES  35 

where  A  is  the  equivalent  conductance  of  the  solution  at  the  concentra- 
tion C,  and  A0  is  the  limiting  value  which  the  conductance  approaches 
as  the  concentration  decreases  without  limit.  According  to  this  theory, 
we  may  calculate  the  fraction  of  electrolyte  in  an  ionized  condition,  if 
we  know  the  equivalent  conductance  and  the  limiting  value  which  the 
equivalent  conductance  approaches  at  zero  concentration.  In  Table  III 
were  given  values  of  the  equivalent  conductance  of  a  number  of  electro- 
lytes at  a  series  of  concentrations.  The  approximate  limiting  values 
A0,  which  the  equivalent  conductance  approaches  at  low  concentrations, 
appear  in  the  second  column  of  that  table.  From  these  values  we  may 
calculate  the  degree  of  ionization  of  the  electrolytes  at  any  concentration 
falling  within  the  intervals  given.  In  the  case  of  potassium  chloride, 
for  example,  A0  =  130.0,  approximately,  and  the  equivalent  conductance 
at  normal  concentration  is  98.22.  Therefore,  the  ionization  of  potassium 
chloride  at  this  concentration  is  approximately  75% ;  that  is,  of  the  total 
potassium  chloride  present  in  solution  at  this  concentration,  75%  is  con- 
cerned in  the  actual  process  of  conduction  and  25%  takes  no  part  in  this 
process. 

The  ionization  values  of  various  electrolytes  in  water  at  18°  are  given 
in  Table  IV.23  It  will  be  observed  that  the  ionization  of  salts  of  the 

TABLE  IV. 
IONIZATION  VALUES  OF  ELECTROLYTES  IN  WATER  AT  18°. 

Concentra- 
tion, C.          10-8  2  x  10-3  5  x  10-3 10-z  2  X  10-2  5  X  10-*  10'1  2  X  10-1  5  X- 10-1  1.0 

NaCl    977  .969  .953  .936  .916     .882     .852     .818     .773     .741 

KC1    979  .971  .956  .941  .922     .889     .860    .827     .779     .742 

Lid 975  .966  .949  .932  .911     .878     .846     .812     .766     .737 

RbCl    980  942  855    748 

CsCl   978  .969  .954  .937  847    

T1C1 976  .965  .942  .915  

KBr 978  .970  .955  .940  .921     .888     .859     .825     .766    .... 

KI 978  .970  .956  .941  .922     .890    .869    773    .727 

KSCN 978  .970  .955  .940  .920     .888     .860    

KF 978  .970  .954  .937  .915     .878    

NaF 974  .964  .945  .925  .899     .854    

T1F 961  .936  .908     .865     

NaK03 977  .968  .950  .932  .910    .871     .832     .788     .719    .660 

»  Noyes  and  Falk,  J.  Am.  Chem.  Soc.  34,  454  (1912). 

In  calculating  the  ionization  at  the  higher  concentrations  Noyes  and  Falk  have  cor- 
rected for  the  viscosity  change  of  the  solution  due  to  the  added  electrolyte.  While  there 
is  every  reason  for  believing  that  the  change  in  the  viscosity  of  the  solution  entails  a 
change  in  the  speed  of  the  carriers,  in  general,  the  change  in  speed  is  probably  not  directly 
proportional  to  the  change  in  the  fluidity  of  the  medium.  All  ionization  values  at  higher 
concentrations,  therefore,  are  more  or  less  in  doubt.  As  a  rule  the  viscosity  effects  are 
small  at  concentrations  below  10'2  N.  In  comparing  the  ionization  of  various  electrolytes, 
therefore,  it  is  best  to  choose  concentrations  at  which  the  viscosity  effect  may  be  neglected. 


36         PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

TABLE  IV.— Continued 

Concentra- 
tion, C.          10-82  X  10-«  5  X  10-'  10-2  2  X  10-2  5  X  10-2  10  J  2  X  10-1  5  X  10-'  1.0 

KN03   978    .970    .953     .935  .911     .867     .824    .772     .688     .613 

LiN03    975     .965     .950    .932  .911     .874     .840    .803     .750    .703 

T1N03 977    .967    .948     .926  843     .788    

AgN03 977    .968    .950    .931  .908    .859    .814    683    .617 

KBr03 980    .970     .954    .934  .910     .868     .830    

KC103 978     .969     .952     .933  .910    .866     .827     .780    .703     .... 

NaI03    971     .960     .939     .917  .890    .842     .801     .752     

KI03    975     .965     .946    .928  .903     .860    .819     .775     

LiIO3 970    .958     .936     .912  .883     .834     .789     .740     .682     .643 

HC1    990    .988     .981     .972  .962     .944    .925     

HN03   992     .987    970  940     .921     

BaCl2 956     883  .850    .798     .759     .720     .672     .642 

CaCl2    954     .938    .910    .882  .849     .802     .764     .727     .686     .662 

MgCl2 955     .939     .910     .883  .851     .803     .765     .728    .687     .669 

PbCl2 943     .917     .865     .808  .738     .627    

CdCl2    931     .891     .803     .735  .664    .559     .453     .375     .289    .217 

CdBr2  .897    .858    .749     .661  .573     

CdI2    870    .809    .675     .573  .469    

Ba(N03)2   .   .953     .934    .898     .861  .818     .744     .679     .609     .504    .... 

Sr(N03)2  ..   .953     .935    .904     .871  .833     .770    .719     .661     .579     .511 

Ca(NO,)2  .   .954    .937     .907    .876  .838    .781     .731     .679     .609     .549 

Mg(N03)2.  .953     .936    .907    .880  .847    .799    .760    .721     

Pb(N03)2   .   .947    .926     .886     .845  .793     .708     .635     .559     .454    .377 

Cd(N03)2  .   .996     .974    .917    .871  .848    .792     .731     .684    .628    .577 

Ba(Br03)2..   .947    .927    .892     .856  .812    

K2S04 954    .937     .905    .872  .832     .771     .722     .673     .618    .592 

Na2S04 939    .925    .893    .857  756    .704    .652    

LiS04 946    854  .811     .744    .688    .633     .567     .528 

T12S04 948     .924    .882     .837  .780    .694    .625     .561     

Ag2S04   949     .927     .885     .840  .784    

K2C204    ...   -960    .945     .916     .886  .849     .795     .753     .711     643 

MgS04 873     .823     .740    .669  .596    .506    .449     .403     349 

ZnS04 854     .799    .710    .633  .556    .464     .405     .360    309 

CdS04 850    .791     .694    .614  .534    .437    .377    .332     .290    .277 

CuS04 862     .804    .709     .629  .550    .455     .396    .351     309 

MgC204  . . .  .582    .472    .350    

K4Fe(CN)6 859    ....     .712  591     .538    .498    

La(N03)3 902    802  701    

K3C6H60T 926    .882    .817  705    

La2(S04)3 464    289  198    

Ca2Fe(CN)6 514    339  ....     .262    

same  type  is  approximately  the  same  at  the  same  concentration.  This 
is  particularly  true  at  the  lower  concentrations  where  the  divergence  in 
many  cases  is  scarcely  greater  than  the  experimental  error.  The  strong 


CONDUCTION  PROCESS  IN  ELECTROLYTES  37 

acids  and  bases,  however,  have  a  markedly  higher  ionization  than  the 
salts.  Salts  of  higher  type  exhibit  a  lower  degree  of  ionization  than 
simpler  salts.  But  here,  again,  salts  of  the  same  type  have  approxi- 
mately the  same  ionization  at  corresponding  concentrations. 

If  electrolytes  approach  complete  ionization  at  low  concentrations 
and  if  the  ions  in  these  solutions  move  independently  of  one  another, 
then,  if  the  transference  numbers  of  the  electrolytes  are  known,  the  value 
of  the  equivalent  conductance  of  the  individual  ions  may  be  calculated. 
If  the  conductances  of  a  sufficient  number  of  pairs  of  electrolytes  have 
been  determined,  it  is  only  necessary  to  know  the  transference  number 
of  a  single  electrolyte.  In  general,  the  values  of  the  ionic  conductances 
are  based  upon  the  transference  number  of  potassium  chloride.  The 
values  of  the  equivalent  conductances  of  various  ions  in  water  at  18°  are 
given  in  Table  V.24 

TABLE  V. 

EQUIVALENT  CONDUCTANCES  OF  THE  INDIVIDUAL  IONS  AT  18°. 

Cs  68.0  Ba   55.4  Cl   65.5 

Rb  67.5  Ca   51.9  N03 61.8 

Tl   65.9  Sr 51.9  SON  56.7 

NH4   64.7  Zn  47.0  C103   55.1 

K   64.5  Cd   46.4  Br03    47.6 

Ag   54.0  Mg   45.9  F    46.7 

Na  43.4  Cu   45.9  I03   34.0 

Li    33.3  La    61.0  S04  68.5 

H   314.5  Br  67.7  C204    63.0 

Pb   60.8  I   66.6  Fe(CN)6   95.0 

The  equivalent  conductance  values  of  the  different  ions  are  of  the 
same  order  of  magnitude,  although  the  values  for  the  hydrogen  and 
hydroxyl  ions  are  markedly  greater  than  for  the  other  ions.  This  is  in 
agreement  with  the  greater  values  of  the  conductance  of  solutions  of 
the  strong  acids  and  bases.  The  conductance  values  of  the  different  ions 
appear  to  bear  no  simple  relation  to  their  constitution.  So,  for  ex- 
ample, lithium,  which  is  lighter  and  has  a  smaller  atomic  volume  than 
the  remaining  alkali  metals,  has  the  lowest  conductance  of  any  of  the 
ions  whose  conductance  values  are  tabulated.  On  the  other  hand,  the 
nitrate  and  the  chloride  ions  have  markedly  higher  values  than  the 
fluoride  ion. 

5.    Molecular  Weight  of  Electrolytes  in  Solution.    The  hypothesis  of 
Arrhenius,  that  the  ionization  of  an  electrolyte  may  be  measured  by  the 

"Noyes  and  Falk,  loc.  cit. 


38          PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

ratio  of  the  equivalent  conductance  at  any  concentration  to  the  limiting 
value  of  the  equivalent  conductance  at  low  concentrations,  is  supported 
by  other  important  properties  of  these  solutions.  Raoult  25  had  observed 
that  the  freezing  point  depression  produced  by  electrolytes  in  water  is 
greater  than  that  of  other  substances  at  equivalent  concentrations,  van't 
Hoff,26  finally,  supplied  the  theoretical  foundation  which  made  it  pos- 
sible to  calculate  from  the  measurements  of  Raoult  the  molecular  weight 
of  substances  in  solution.  Since  in  the  case  of  aqueous  salt  solutions  the 
depression  was  found  to  be  abnormal,  van't  Hoff  introduced  an  arbitrary 
factor  i,  which  he  apparently  assumed  to  be  a  constant  independent  of 
concentration.  Arrhenius  at  once  recognized  the  significance  of  van't 
Hoff's  factor  and  pointed  out  the  relation  between  this  factor  and  the 
coefficients  derived  from  conductance  measurements.  According  to 
Arrhenius,  if  electrolytes  are  dissociated,  the  freezing  point  depression  of 
their  solutions  as  measured  should  be  greater  than  that  calculated  ac- 
cording to  the  method  of  van't  Hoff,  the  molecular  weight  being  assumed 
equal  to  the  formula  weight  of  the  dissolved  substance.  If  we  let 

M 


where  M  is  the  formula  weight  and  MQ  the  molecular  weight  calculated 

from  freezing  point  measurements,  then,  obviously,  there  exists  between 
i  and  y>  the  relation: 

(4)  t=l+(n—  lh, 

where  n  is  the  number  of  ions  resulting  from  the  dissociation  of  a  single 
molecule.  The  values  of  y  as  calculated  from  freezing  point  or  other 
similar  determinations  should  thus  agree  with  the  values  of  y  as  calcu- 
lated from  conductance  measurements.  In  Table  VI  27  are  given  the 

TABLE  VI. 

COMPARISON  OF  IONIZATION  VALUES  DERIVED  FROM  CONDUCTANCE  AND 
FROM  FREEZING  POINT  MEASUREMENTS. 

Electrolyte        Method  5  X  10a     10-2     2  X  10-2    5  X  10-2   10-1  2  X  10-1  5  X  10-1 

KC1    ........  ...     F  .963  .943  .918  .885  .861  .833  .800 

C  .956  .941  .922  .889  .860  .827  .779 

NH4C1    .........     F  .947  .928  .907  .878  .856  .832  .... 

C  .941  .921 


"  C.  R.  94,  1517;  95,  188  and  1030   (1882). 

»«  van't  Hoff,  8v.  Vet.-Akad.  Handlingar  91,  No.  17   (1886),  p. 

"Noyes   and   Falk,  J.   Am.   Chem.   8oc.   3J,,   485    (1912).     Th< 


148. 
e  concentrated   solutions 
have  been  corrected  for  the  viscosity  effects.      (See  footnote  above,  p.  35.) 


CONDUCTION  PROCESS  IN  ELECTROLYTES  39 

TABLE   VI.— Continued 
Electrolyte        Method    5  X  10-'      10 J      2  X 10-2    5  X 10-'      10-1      2  X 10-1  5  X 10-1 


NaCl     

..     F 

.953 

.938 

.922 

.892 

.875 

.850 

.824 

CsCl   

C 
..     F 

.953 

.936 

.916 
.930 

.882 
.892 

.852 
.863 

.818 
.829 

.773 

.778 

Lid     

C 
..     F 

.954 
.944 

.937 
.937 

^928 

.912 

.847 
.901 

KBr  

C 
..     F 

.949 

.932 

.890 
.929 

.878 
.889 

.846 
.863 

.812 
.839 

.766 
.813 

NaN03    

C 
..     F 

.955 

.940 
.903 

.921 
.885 

.888 
.855 

.859 
.830 

.825 
.798 

.766 

KNOg  

C 
...     F 

.950 

.932 
.901 

.910 
.880 

.871 
.836 

.832 
.781 

.788 
.711 

.719 

KC10 

C 

..    F 

.953 

.935 
914 

.911 
891 

.867 
849 

.824 
798 

.772 

.688 

KBrO 

C 
.     F 

.952 

.933 
923 

.910 
896 

.866 
854 

.827 
805 

.780 

.703 

C 

.954 

.934 

.910 

.868 

KI03   

...     F 

.941 

.913 

.882 

.828 

.765 

NaIOs    

C 
...     F 

.946 
.939 

.928 
.916 

.903 
.890 

.860 
.842 

.819 
.773 

.775 

.... 

KMn04  , 

C 
...     F 

.939 
.938 

.917 
.921 

.890 
.913 

.842 

.801 

.752 

•  ... 

C 

.968 

.951 

.930 

HC1   

...     F 

.991 

.975 

.957 

.933 

.917 

HN03    

C 
...    F 

.981 
.974 

.972 
.960 

.962 
.942 

.944 
.912 

!900 

879 

••  •  • 

C 

.970 

.940 

BaCl2  

...     F 

.899 

.878 

.855 

.819 

788 

758 

CaCl2   

C 

...     F 

.883 

.850 
.876 

.798 
.837 

.759 
815 

.720 
804 

.672 

MgCL 

C 
...     F 

.910 

.882 

.849 
.885 

.802 
.854 

.764 
.839 

.727 
.833 

.688 

CdCl2   

C 
...     F 

.910 

.883 
.791 

.851 
.768 

.803 
.690 

.765 
.605 

.728 
539 

.687 

CdBr2 

C 
...     F 

.803 

.735 

.780 

.664 
.704 

.559 
.589 

.453 
.482 

.375 
367 

.289 

C 

.749 

.661 

.573 

CdL 

...     F 

.593 

.540 

.400 

225 

100 

C 

.675 

.573 

.469 

Cd(NO«)2 

...     F 

.948 

.921 

.901 

887 

884  • 

Ba(N03)2  ... 

C 
...     F 

.917 
.917 

.871 

.888 

.848 
.855 

.792 

.731 

.684 

.628 

PbCNCU, 

C 

...     F 

.898 
.890 

.861 
.850 

.818 
.804 

.744 
724 

.679 
649 

.609 
568 

.504 

497 

K2S04   

C 
...     F 

.886 
.929 

.845 
899 

.793 

857 

.708 
785 

.635 
730 

.559 
667 

.454 
^fi« 

C 

.905 

.872 

.832 

.771 

.722 

.673 

.618 

40        'PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

TABLE   VI.— Continued 
Electrolyte        Method    5X10-3      10  J      2X10-2    5X10-2      10-1      2X10-1  5X10-1 


Na  S04       .  .   . 

..    F 

.867 

.795 

.736 

.672 

.567 

MgSCX, 

C 

..    F 

.893 
.694 

.857 
.618 

.756 
.420 

.704 
.324 

.652 
.223 

OuSO 

C 
F 

.740 
616 

.669 
545 

.596 
455 

.506 
.318 

.449 

.403 

.... 

ZnSO 

C 
F 

.709 
665 

.629 
582 

.550 
489 

.455 

.396 

.351 

.... 

CdS04   

C 

..     F 

.710 
.658 

.633 
.569 

.556 
.477 

.464 
.343 

.405 

.360 

.... 

"K"  TJWP.'Nn 

C 
F 

.694 
894 

.614 

868 

.534 

778 

.437 

.377 

.332 

.290 

G 

869 

827 

K4Fe(CN)e  ... 

..     F 

.634 

.581 

.520 

.425 

C 

.. 

.... 

•  •  •  • 

.591 

.538 

.498 

values  of  y  as  determined  from  freezing  point  (F)  and  from  conductivity 
(C)  measurements. 

It  will  be  observed  that  in  the  case  of  certain  electrolytes  the  values 
of  y  derived  by  the  two  methods  correspond  very  closely.  This  is  par- 
ticularly true  of  potassium  chloride  where  the  two  values  correspond 
practically  within  the  limit  of  experimental  error  up  to  concentrations  as 
high  as  0.1  normal.  In  the  case  of  other  salts,  the  divergence  at  higher 
concentrations  is  considerably  greater.  In  general,  however,  the  two 
values  approach  each  other  the  more  nearly,  the  lower  the  concentration 
of  the  solution.  The  correspondence  between  the  two  values  is  closest 
in  the  case  of  the  binary  salts.  The  more  complex  a  salt,  the  greater  is, 
as  a  rule,  the  divergence  between  the  two  values  and  the  lower  the  con- 
centration at  which  a  given  divergence  appears. 

The  cause  of  the  divergence  of  the  ionization  values  as  determined 
by  the  two  methods  is  as  yet  uncertain.  It  is  possible  that  the  ionization 
is  not  correctly  measured  by  the  conductance  ratio.  At  higher  concen- 
trations, at  any  rate,  it  is  to  be  expected  that  various  influences  will  make 
themselves  felt,  such  as  the  effect  of  viscosity,  as  a  result  of  which  the 
conductance  as  measured  will  not  yield  a  true  measure  of  the  ionization. 
On  the  other  hand,  the  molecular  weight,  as  determined  by  osmotic 
methods,  may  be  expected  to  be  in  error,  since  the  laws  of  dilute  solu- 
tions are  assumed  in  calculating  these  values.  The  only  assurance  we 
have  that  the  laws  of  dilute  solutions  are  applicable  under  given  condi- 
tions is  that  the  results  obtained  are  in  agreement  with  other  facts  re- 
lating to  these  solutions.  When  a  disagreement  occurs,  therefore,  it  is 


CONDUCTION  PROCESS  IN  ELECTROLYTES  41 

not  known  whether  the  laws  of  dilute  solutions  are  inapplicable  or 
whether  some  other  discrepancy  has  arisen. 

In  the  case  of  salts  of  higher  type,  and  even  in  that  of  the  simpler 
types  of  salts,  there  is  always  a  possibility  that  the  ionization  process  as 
assumed  in  calculating  the  ionization  from  conductance  measurements 
does  not  correspond  to  the  true  reaction.  For  example,  in  calculating  the 
ionization  of  barium  chloride,  it  is  assumed  that  the  reaction  takes  place 
according  to  the  equation: 

BaCl2  =  Ba"  +  2CK 

It  is  possible,  however,  that  ionization  may  take  place  in  several  stages, 
an  intermediate  reaction  of  the  type: 

BaCl2  =  BaCl+  +  Cl- 

intervening.  If  an  intermediate  reaction  of  this  type  takes  place,  then 
it  is  obviously  impossible  to  calculate  the  degree  of  ionization  from  con- 
ductance measurements.  So  far,  it  has  proved  difficult  to  establish  the 
existence  of  intermediate  ions.  In  general,  it  is  to  be  expected  that  if 
intermediate  ions  exist,  the  transference  numbers  will  vary  markedly 
with  the  concentration.  It  should  be  noticed  in  this  connection  that 
those  electrolytes,  which  exhibit  the  greatest  divergence  between  the 
ionization  values  as  calculated  from  conductance  and  from  freezing  point 
data,  also  exhibit  a  marked  change  in  their  transference  numbers  with 
change  of  concentration.  In  the  case  of  sulphuric  acid 28  the  existence  of 
an  intermediate  ion  has  been  definitely  established;  and  various  consid- 
erations, based  upon  the  solubility  of  salts  in  the  presence  of  other  salts, 
lend  support  to  the  view  that  intermediate  ions  exist  in  solutions  of 
many  salts  of  higher  type.29 

In  any  case,  it  is  important  to  note  that  the  values  of  i  as  deter- 
mined from  freezing  point  and  from  conductivity  determinations  appar- 
ently approach  the  same  limit  at  low  concentrations,  and,  moreover,  the 
limits  approached  are  in  agreement  with  the  constitution  of  the  salts  in 
question.  So,  for  example,  in  the  case  of  the  binary  electrolytes,  the 
limit  approached  is  2,  in  that  of  ternary  electrolytes  3,  in  that  of  quater- 
nary salts  4,  etc.  No  case  has  been  observed  in  which  the  limit  ap- 
proached is  greater  than  that  corresponding  to  the  constitution  of  the 
salt. 

6.  Applicability  of  the  Law  of  Mass  Action  to  Electrolytic  Solutions. 
On  their  surface,  the  results  of  conductance  and  of  freezing  point  meas- 
urements appear  to  be  in  substantial  agreement  with  the  fundamental 

M  Noyes  and  Eastman,  Carnegie  Report  No.  19,  p.  241. 
»Harkins,  J.  Am.  Chem.  Soc.  5Sf  1808  (1911). 


42          PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

hypothesis  of  Arrhenius;  namely,  that  an  electrolyte  in  solution  is  ion- 
ized, and  its  ionization  is  a  function  of  the  concentration,  decreasing  with 
increasing  concentration.  There  exists,  therefore,  in  solutions  of  electro- 
lytes an  equilibrium  between  the  ions  and  the  un-ionized  molecules,  and 
this  equilibrium  must  be  subject  to  the  usual  laws  governing  equilibria. 
It  is  obvious  that,  according  to  the  law  of  mass  action,  the  ionization 
should  increase  with  decreasing  concentrations,  since  there  is  an  increase 
in  the  number  of  molecular  species  as  a  result  of  the  reaction.  If  we 
assume  a  simple  system,  as  for  example  a  binary  salt  MX  which  forms 
the  ions  M+  and  X~,  according  to  the  equation: 

MX  =  M+  +  X-, 
then,  according  to  the  law  of  mass  action,  we  should  have  a  relation: 


(5) 


, 

CMX 

where  C^  represents  the  concentration  of  the  molecular  species  X.    If 

the  solution  is  sufficiently  dilute,  so  that  the  laws  of  dilute  solutions  may 
be  applied,  then  K  will  be  a  function  of  the  temperature  only.  On  the 
other  hand,  it  is  obvious  that  a  concentration  must  ultimately  be  reached 
where  the  laws  of  dilute  solutions  fail,  in  which  case  K  becomes  a  func- 
tion of  the  concentration  as  well  as  of  the  temperature.30 

If  y  is  the  degree  of  ionization  of  the  salt  and  if  C  is  its  total  concen- 
tration, then  the  concentrations  of  the  two  ions  will  be  equal  to  Cy  and 
the  concentration  of  the  un-ionized  fraction  will  be  equal  to  C(l  —  y).  If 
these  values  are  substituted  in  Equation  (5),  they  lead  to  the  equation: 

(6) 

The  value  of  y  mav  be  calculated  either  from  conductance  or  from 
osmotic  measurements.  If  the  values  of  y  according  to  the  two  methods 
agree,  then  obviously  the  two  methods  must  lead  to  identical  results,  so 
far  as  the  mass-action  law  is  concerned.  Since  the  degree  of  ionization 
is  given  by  Equation  2,  we  may  substitute  this  value  of  y  in  Equation  6 
which  yields  the  equation: 

m  CA2        _ 

A0(A0_A)-X- 

This  equation,  involving  the  two  constants  K  and  A0,  therefore  expresses 
the  relation  between  the  concentration  and  the  conductance  of  a  solution 

80  Van  der  Waals-Kohnstamm,  "Lehrbuch  der  Thermodynamik,"  part  2,  pp.  604, 
et  seq. 


CONDUCTION  PROCESS  IN  ELECTROLYTES  43 

of  a  binary  electrolyte.  In  general,  to  test  the  applicability  of  this 
equation,  the  value  of  A0  must  first  be  determined  by  some  method  of 
extrapolation,  after  which  the  constancy  of  the  function  K  may  be 
determined  by  substituting  in  the  above  equation.  In  Table  VII 31  are 

TABLE  VII. 
VALUES  OF  K  FOR  ACETIC  Aero  IN  WATER  AT  25°. 

V  A  K  X 100 

0.989  1.443  0.001405 

1.977  2.211  0.001652 

3.954  3.221  0.001759 

7.908  4.618  0.001814 

15.816  6.561  0.001841 

31.63  9.260  0.001846 

63.26  13.03  0.001846 

126.52  '  18.30  0.001847 

253.04  25.60  0.001843 

506.1  35.67  0.001841 

1012.2  49.50  0.001844 

2024.4  68.22  0.001853 

oo  387.9         — 

given  values  for  the  conductance  of  acetic  acid  in  water  at  25°  at  a 
series  of  concentrations.  In  this  table,  V  denotes  the  dilution  in  liters 
per  equivalent,  A  the  equivalent  conductance  and  K  the  ionization  con- 
stant, calculated  according  to  Equation  7. 

It  will  be  seen  that  at  higher  concentrations,  down  to  about  0.1  nor- 
mal, there  is  a  marked  change  in  the  value  of  the  function  K,  but  at 
concentrations  below  0.1  normal  the  function  K  remains  constant,  prac- 
tically within  the  limits  of  experimental  error.31*  At  the  highest  dilution 
in  the  table  the  function  K  shows  a  slight  increase,  which  is  probably 
due  to  a  discrepancy  between  the  experimental  values  and  the  assumed 
value  of  A0.  In  general,  the  weaker  the  acid,  the  greater  the  range  of 
concentration  over  which  the  function  K  remains  constant.  In  other 
words,  the  concentration,  at  which  the  function  K  varies  measurably 
from  constancy,  increases  as  the  strength  of  the  acid  increases.  In  Table 
VIII 32  are  given  values  of  the  equivalent  conductance  and  the  ionization 
constant  of  trichlorobutyric  acid  at  a  series  of  concentrations.  It  will  be 

11  Kendall,  Med.  Veten.  Aka4.  Nobelinstitut  2,  No.  38,  p.  1   (1913). 

»ia  The  decrease  in  the  value  of  K  at  higher  concentrations  is  in  part,  if  not  largely, 
due  to  the  increasing  viscosity  of  the  solution.  Compare  Washburn,  "Principles  of  Physi- 
cal Chemistry,"  2nd  Ed.,  p.  340. 

«a  Kendall,  loc.  cit. 


44          PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

TABLE  VIII. 
VALUES  OF  K  FOR  TRICHLOROBUTYRIC  ACID  IN  WATER  AT  25°. 

V  A  K  X 100 

5.90  237.3  18.3 

11.80  276.8  17.4 

23.59  308.5  15.9 

38.63  326.4  14.8 

47.18  331.8  14.0 

53.98  336.0  13.9 

77.26  343.9  12.7 

107.96  350.4  11.8 

154.5  357.0  11.5 

215.9  361.2  10.9 

309.0  365.1  10.5 

431.8  368.2  10.7 

618.0  370.9  (11.6) 

oo  376.0*  — 

observed  that  the  function  K  decreases  throughout  as  the  concentration 
decreases,  but  that  the  decrease  is  more  marked  at  higher  concentrations 
and  that,  apparently,  at  lower  concentrations  a  limiting  value  is  ap- 
proached. The  slight  variation  in  the  value  of  K  at  the  lowest  con- 
centrations may  be  due  either  to  experimental  errors  or  to  a  discrepancy 
in  the  value  of  A0.  In  general,  we  may  say  that  electrolytes,  such  as 
acetic  acid,  fulfill  the  condition  that  in  the  more  dilute  solutions  the 
function  K  remains  substantially  constant.  The  same  holds  true  in  the 
case  of  the  weak  bases. 

Obviously,  these  results  afford  strong  confirmative  evidence  of  the 
correctness  of  the  fundamental  assumption  that  these  electrolytes  are 
ionized  in  solution  according  to  a  reaction  equation  of  the  following  type: 

CH3COOH  =  CH3COO-  +  H+. 

On  the  other  hand,  when  we  proceed  to  a  consideration  of  typical  salts, 
or  what  are  commonly  known  as  strong  electrolytes,  we  find  that  K  ap- 
pears throughout  to  be  a  function  of  the  concentration,  its  value  decreas- 
ing as  the  concentration  decreases. 

Below  are  given  the  values  of  the  function  K  at  a  series  of  concen- 
trations for  solutions  of  potassium  chloride  in  water  at  18°: 33 

"  The  manner  in  which  K  varies  with  the  concentration  at  very  low  concentrations 
is  uncertain,  since  small  errors  in  the  extrapolated  value  of  A0  cause  a  large  variation 
in  the  resulting  value  of  the  function  K.  The  values  here  given  are  based  on  the  va 
A0  derived  by  the  author.  J.  Am.  Chem.  Soc.  W,\  (1920).  Compare,  also,  Weiland, 


CONDUCTION  PROCESS  IN  ELECTROLYTES  45 

TABLE  IX. 

VALUES  OF  K  FOR  KC1  IN  WATER  AT  18°. 

c=    io-5       io-4       io-3       io-2       lo-1       i.o 

K=.  00518        .0147        .0474        .1542        .5052        2.14 

It  will  be  observed  that  in  this  case  the  function  K  decreases  enormously 
with  decreasing  concentration.  Whether  the  function  approaches  a  finite 
limit,  or  whether  it  approaches  a  limit  zero  at  low  concentrations,  cannot 
be  determined  with  certainty.  In  general,  the  stronger  the  electrolyte, 
the  more  does  the  function  K  vary  with  the  concentration  and  the 
greater  is  its  value  at  a  given  concentration.  In  the  case  of  hydrochloric 
acid  the  values  of  .K  at  a  number  of  concentrations  are  as  follows: 

TABLE  X. 
VALUES  OF  K  FOR  HC1  IN  WATER  AT  18°. 

c=  io-3  io-2  io-1 

K  =  0.189  0.366  1.11 

If  these  values  are  compared  with  those  for  potassium  chloride,  it  will  be 
seen  that  the  value  of  K  is  considerably  greater  for  hydrochloric  acid 
than  it  is  for  potassium  chloride.  At  0.1  normal  the  value  of  K  for 
hydrochloric  acid  is  approximately  twice  that  for  potassium  chloride. 
In  the  more  dilute  solutions,  however,  this  ratio  appears  to  increase,  since 
in  a  0.001  normal  solution  the  value  for  hydrochloric  acid  is  approxi- 
mately four  times  that  of  potassium  chloride. 

In  view  of  the  fact  that  electrolytes  of  a  given  type  appear  to  be 
ionized  to  practically  the  same  extent  in  water,  it  follows  that  the  dis- 
crepancies found  for  different  electrolytes  of  the  same  type  will  be  of 
the  same  order  of  magnitude. 


Chapter  III. 

The  Conductance  of  Electrolytic  Solutions  in  Various 

Solvents. 

1.  Characteristic  Forms  of  the  Conductance-Concentration  Curve. 
The  property  of  forming  solutions  which  possess  the  power  of  con- 
ducting the  current  is  one  not  restricted  to  water.  Nor,  indeed,  are 
electrolytes  in  non-aqueous  solvents  restricted  entirely  to  those  sub- 
stances which  are  electrolytes  in  aqueous  solution.  As  the  field  of  non- 
aqueous  solutions  has  been  extended  in  recent  years,  it  has  become  more 
and  more  apparent  that  the  property  of  forming  solutions  which  conduct 
the  current  is  one  which  is  common  to  a  great  many  substances.  Indeed, 
it  seems  not  improbable  that  all  liquid  non-metallic  media  yield  elec- 
trolytic solutions  when  suitable  substances  are  dissolved  in  them. 

In  attempting  to  account  for  the  properties  of  electrolytic  solutions  in 
water,  it  is  difficult  to  distinguish  between  those  properties  which  are 
characteristic  of  electrolytic  solutions  in  general  and  those  which  are 
characteristic  of  aqueous  'solutions  alone.  Such  a  knowledge  can  be 
obtained  only  from  a  study  of  the  properties  of  electrolytic  solutions  in  a 
large  variety  of  solvents,  and  it  appears  unlikely  that  the  properties  of 
electrolytic  solutions  may  be  successfully  accounted  for  until  we  possess 
reliable  data  as  to  the  properties  of  non-aqueous  solutions.  While  this 
field  has  been  greatly  extended  during  the  past  two  decades,  it  is  only  in 
the  case  of  a  few  solvents  that  we  possess  a  sufficient  mass  of  facts  to 
enable  us  to  treat  the  subject  with  a  measurable  degree  of  completeness. 

From  a  constitutional  point  of  view,  the  alcohols  are  more  nearly 
related  to  water  than  are  any  other  solvents,  since  they  may  be  looked 
upon  as  water  in  which  one  of  the  hydrogen  atoms  has  been  substituted 
by  a  hydrocarbon  group.  We  should  expect  the  properties  of  these 
solvents  to  diverge  progressively  from  those  of  water  as  the  size  and 
complexity  of  the  hydrocarbon  group  increases,  and  such  has  indeed  been 
found  to  be  the  case.  In  general,  the  ionizing  power  of  the  alcohols 
diminishes  as  the  complexity  of  the  carbon  group  increases.  Accord- 
ingly, methyl  alcohol  stands  much  nearer  to  water  than  do  any  of  the 
other  representatives  of  this  class  of  solvents. 

For  the  purposes  of  illustration  we  may  consider  the  conductance  of 

46 


ELECTROLYTIC  SOLUTIONS  IN  VARIOUS  SOLVENTS  47 

sodium  iodide  in  ethyl  alcohol,  the  values  of  which  are  given  in  Table 
XI:1 

TABLE  XI. 

CONDUCTANCE  OF  SODIUM  IODIDE  IN  ETHYL  ALCOHOL  AT  18°. 

V  125         250         500       1000       2000       4000       8000        oo 

A  28.6        31.3        33.5        35.2        36.5        37.6        38.3      39.4 

Y  0.726      0.794      0.850      0.894      0.926      0.954      0.972        1.0 

It  will  be  observed  that  the  conductance  of  solutions  in  ethyl  alcohol 
increases  with  decreasing  concentration  in  a  manner  similar  to  that 
of  solutions  in  water.  The  limiting  value  of  the  equivalent  conductance, 
that  is  the  value  of  A0,  for  a  solution  of  sodium  iodide  in  ethyl  alcohol 
is  in  the  neighborhood  of  39.4.  It  follows,  therefore,  that  the  ionization 
values  of  solutions  in  ethyl  alcohol  are  considerably  smaller  than  those 
of  solutions  in  water.  In  Figure  3,  the  ionization  of  sodium  iodide  in 
ethyl  alcohol  is  shown  as  a  function  of  concentration.  In  the  same  figure, 
the  ionization  of  sodium  chloride  in  water  is  likewise  shown. 

Acetone  is  another  solvent  whose  solutions  resemble  those  in  water 
in  many  respects.  The  conductance  of  sodium  iodide  in  acetone  at  18° 
at  a  series  of  concentrations  is  given  in  Table  XII:  2 

TABLE  XII. 

CONDUCTANCE  OF  SODIUM  IODIDE  IN  ACETONE  AT  18°. 

V  ....  292.6       1030       4083       8874     18660     39700     64827          oo 
A   ....   112.8      131.1       147.7      151.0      154.8      155.2       156.0?     156.0 
Y 0.723      0.841      0.947      0.968      0.992      0.995 

Here,  again,  it  will  be  observed  that  the  equivalent  conductance  rises 
throughout  with  decreasing  concentration.  While  the  conductance  values 
of  acetone  solutions  are  greater  than  those  of  solutions  in  ethyl  alcohol, 
the  degree  of  ionization  is  very  nearly  the  same  in  the  two  solvents.  In 
both  ethyl  alcohol  and  acetone  the  ionization  is  much  lower  than  it  is  in 
water. 

Another  typical  solvent  is  found  in  liquid  sulphur  dioxide.  The  con- 
ductance values  of  solutions  of  potassium  iodide  in  sulphur  dioxide  at 
—  33°  and  at  — 10°  are  given  in  Table  XIII: 3 

1Dutoit  and  Rappeport,  Jour.  d.  Chim.-Phys.  6,  545   (1908). 
1  Dutoit  and  Levrier,  Jour.  d.  Chim.-Phys.  3.  43  (1905), 
•Franklin,  J.  Pliys.  Chem.  15,  675   (1911), 


48 


PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 
1.00 


•90 


.80 


I 

I 

I!    .70 


.60 


.50 


o.o 


3.0 


4.0 


l.O  2.O 

Log  V. 

FIG.  3.    lonization  of  Binary  Electrolytes  in  Different  Solvents. 

TABLE  XIII. 
CONDUCTANCE  OF  KI  IN  SO,  AT  — 33°  AND  — 10°. 


—  33C 

—  10C 


0.50 
27.5 
39.7 


1.00 
37.7 
46.9 


2.0 
40.1 
46.8 


4.0 
40.5 
44.8 


8.0 
41.0 
42.5 


16.0 
42.7 
43.5 


32.0  64.0 
47.2  55.1 
47.8  55.7 


V  128.0    256.0    512.0     1000.0    2000.0    4000.0    8000.0       cx> 


—  33C 

—  10C 


65.9 
66.5 


78.8 
81.7 


93.4 
99.2 


108.6 
118.8 


124.2 
140.5 


139.0 
162.5 


153.0    167.5 
181.8    199.0 


Again,  we  find  that  as  the  concentration  decreases  the  equivalent  con- 
ductance increases  and  approaches  a  limiting  value  in  the  neighborhood 
of  167.5  at  — 33°.  The  ionization  of  the  solutions  of  potassium  iodide 
in  sulphur  dioxide  is,  however,  markedly  lower  than  that  of  correspond- 


ELECTROLYTIC  SOLUTIONS  IN  VARIOUS  SOLVENTS  49 

ing  solutions  in  acetone  and  alcohol.  At  higher  concentrations  the  solu- 
tions of  potassium  iodide  exhibit  a  marked  divergence  from  the  aqueous 
type.  While  it  is  true  that  at  —33°  the  conductance  falls  throughout 
as  the  concentration  increases,  it  will  be  observed  that  in  the  concentra- 
tion interval  between  V  =  2  and  V  =  16  the  conductance  undergoes  only 
an  inappreciable  increase,  whereas  at  both  higher  and  lower  concentra- 
tions the  conductance  change  is  quite  marked.  This  behavior  of  the 
more  concentrated  solutions  in  sulphur  dioxide  indicates  the  appearance 
of  a  new  type  of  curve.  At  a  slightly  higher  temperature  this  irregu- 
larity at  the  higher  concentration  becomes  more  pronounced  and  a  maxi- 
mum and  a  minimum  occurs  in  the  curve,  as  may  be  seen  from  the  values 
given  for  the  conductance  of  these  solutions  at  —10°.  The  curve  at 
— 10°  is  a  typical  example  which  is  met  with  in  the  case  of  a  large 
number  of  solvents. 

Before  discussing  this  case  in  detail,  however,  let  us  examine  a  type 
of  solution  the  conductance  curve  of  which  has  a  form  radically  different 
from  that  of  aqueous  solutions.  In  Table  XIV  4  are  given  values  of  the 
conductance  of  methyl  alcohol  in  liquid  hydrogen  bromide  at  —90°. 

TABLE  XIV. 
CONDUCTANCE  OF  CH3OH  IN  LIQUID  HBr  AT  — 90°. 

V 0.1250    0.2500    0.500    0.769       1.00          2.00  7.69 

A  0.600      0.631       0.211     0.0378    0.00925    0.001660    0.000615 

It  will  be  observed  that  in  the  more  dilute  solutions  the  conductance 
diminishes  continuously  as  the  concentration  decreases.  There  is  no  in- 
dication that,  at  lower  concentrations,  the  conductance  approaches  a 
limiting  value  other  than  zero.  In  the  more  concentrated  solutions  the 
conductance  increases  greatly  as  the  concentration  increases,  until  a 
maximum  is  reached,  after  which  the  conductance  falls  off  sharply.  It 
is  interesting  to  note  also  that,  in  this  solvent,  methyl  alcohol  functions 
as  an  electrolyte,  although  in  most  solvents  methyl  alcohol  exhibits  no 
electrolytic  properties.  Actually,  however,  the  solutions  of  methyl  alcohol 
in  hydrogen  chloride  do  not  differ  materially  in  properties  from  solutions 
of  typical  salts,  such  as  the  substituted  ammonium  salts  in  this  solvent, 
although  the  value  of  the  equivalent  conductance  is  larger  for  typical 
salts. 

Another  example  of  this  type  of  conductance  curve  is  that  of  solu- 
tions of  trimethylammonium  chloride  in  liquid  bromine.  The  values  of 
the  conductance  at  25°  are  given  in  Table  XV:  5 

'Archibald,  J.  Am.  Chem.  Soc.  29,  665   (1907). 
"Darby,  J.  Am.  Chem.  Soc.  40,  347   (1918). 


50         PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

TABLE  XV. 
CONDUCTANCE  OF  TRIMETHYLAMMONIUM  CHLORIDE  IN  BROMINE  AT  25°. 

C  .  .  0.029  0.0595  0.2093  0.3427  0.5334  0.9323  1.236  1.314 
A  0.0253  0.1038  2.063  5.259  6.469  9.865  11.49  11.00 

This  case  is,  if  anything,  even  more  extreme  than  that  of  methyl  alcohol 
in  hydrogen  bromide.  The  increase  in  the  conductance  with  increasing 
concentration  is  extremely  marked.  At  a  concentration  of  0.029  mols 
per  liter,  the  equivalent  conductance  is  only  0.0253,  whereas  at  a  concen- 
tration of  1.236  mols  per  liter  the  equivalent  conductance  is  11.49.  It  is 
to  be  noted  that  in  the  neighborhood  of  normal  the  equivalent  conduct- 
ance of  these  solutions  in  bromine  is  comparable  with  that  of  solutions  in 
ordinary  solvents.  At  slightly  lower  concentrations,  however,  this  is  no 
longer  the  case.  For  a  concentration  change  in  the  ratio  of  43  to  1,  the 
conductance  increases  in  the  ratio  of  approximately  450  to  1. 

It  is  apparent  that  the  relation  between  the  conductance  and  the 
concentration,  as  we  observe  it  in  aqueous  solutions,  is  not  a  property 
characteristic  of  electrolytic  solutions  in  general.  It  represents  one  ex- 
treme of  two  types  of  solutions,  the  other  of  which  is  exemplified  in 
solutions  in  hydrogen  bromide  and  in  bromine.  Between  these  two  ex- 
treme types  we  have  an  intermediate  type  which  appears  to  combine 
the  characteristics  of  these  extreme  types.  A  typical  example  is  fur- 
nished by  solutions  of  potassium  iodide  in  methylamine  at  — 33°,  values 
of  which  are  given  in  Table  XVI: 6 

TABLE  XVI. 
CONDUCTANCE  OF  KI  IN  CH3NH2  AT  —  33°. 

V  ....  0.6094  1.190  2.320  8.833  33.62  107.4  408.9  1557  5927 
A  ....  31.12  32.97  28.49  17.40  14.64  17.72  27.79  45.86  74.53 

The  conductance  curve  in  this  case  is  intermediate  in  type  between  that 
of  solutions  in  water  and  in  bromine.  In  the  more  dilute  solutions,  be- 
ginning at  a  dilution  of  approximately  33  liters,  the  conductance  increases 
continuously  with  decreasing  concentration  and  apparently  approaches 
a  limiting  value.  At  a  dilution  of  33.62  liters,  the  conductance  has  a 
minimum  value.  At  higher  concentrations  it  increases  markedly,  reach- 
ing a  maximum  in  the  neighborhood  of  1.19  liters,  after  which  it  again 
decreases.  In  the  more  concentrated  solutions,  therefore,  the  curve  re- 
sembles that  of  solutions  in  bromine. 

•Fitzgerald,  J.  Phya.  Chem.  16,  621  (1912). 


ELECTROLYTIC  SOLUTIONS  IN  VARIOUS  SOLVENTS  51 

These  intermediate  curves  apparently  form  a  continuous  series  be- 
tween the  two  extreme  types  and,  by  suitably  changing  the  condition  of 
the  solutions,  a  continuous  shift  takes  place  in  the  curve  from  one  ex- 
treme toward  the  other.  For  example,  as  the  temperature  of  a  solution 
is  increased,  there  is  a  shift  from  the  aqueous  type  toward  the  type 
exemplified  by  the  solutions  in  hydrogen  bromide.  This  is  clearly  the 
case  with  solutions  in  sulphur  dioxide.  As  we  have  already  seen,  at 
—33°  the  conductance  of  solutions  in  sulphur  dioxide  increases  continu- 
ously with  decreasing  concentration,  although  there  is  a  certain  concen- 
tration interval  over  which  the  conductance  change  is  extremely  small. 
At  a  temperature  of  — 10°  this  curve  exhibits  a  maximum  and  a  mini- 
mum, similar  to  that  just  described  in  the  case  of  solutions  in  methyl- 
amine.  At  still  higher  temperatures,  the  maximum  and  minimum  be- 
come more  pronounced. 

Methylamine  may  be  looked  upon  as  a  derivative  of  ammonia  and 
the  relation  between  methylamine  and  ammonia  solutions  may  be  ex- 
pected to  be  similar  to  that  between  the  alcohols  and  water.  As  we 
shall  see  presently,  ammonia  solutions,  for  the  most  part,  belong  to  the 
aqueous  type;  that  is,  the  conductance  increases  throughout  with  de- 
creasing concentration.  In  the  case  of  methylamine  solutions,  as  we 
have  seen,  the  curve  exhibits  a  pronounced  maximum  and  minimum. 
Solutions  in  ethylamine  are  still  further  removed  toward  the  bromine 
type,  as  is  apparent  from  the  values  given  for  the  conductance  of  silver 
nitrate  in  ethylamine  in  Table  XVII:  T 

TABLE  XVII. 
CONDUCTANCE  OF  AgN03  IN  C2H5NH2  AT  — 33°. 

V  0.9928        1.981        3.953        15.73        62.65        125.0 

A  5.67  5.820        4.320          1.677        1.038          1.041 


In  this  case  the  conductance  decreases  with  decreasing  concentration,  but 
it  is  evident  that  at  the  lower  concentrations  the  conductance  does  not 
approach  the  value  zero  as  a  limit.  In  fact,  it  is  apparent  that,  at  dilu- 
tions slightly  greater  than  125  liters  per  mol,  the  conductance  curve  will 
again  rise.  Indeed,  solutions  of  certain  other  salts  in  ethylamine  exhibit 
a  distinct  minimum  in  the  neighborhood  of  0.01  normal.  The  conductance 
curve  of  solutions  in  amylamine  resembles  that  of  solutions  in  bromine 
very  closely,  the  conductance  decreasing  throughout  with  decreasing  con- 
centration and  apparently  approaching  a  value  of  zero  so  far  as  has 
been  observed. 

T  Fitzgerald,  Joe.  ctt. 


52          PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

It  is  evident  that,  in  order  to  account  for  the  phenomena  of  electro- 
lytic solutions,  it  is  necessary  to  take  into  consideration  the  fact  that 
the  form  of  the  conductance  curve  as  observed  in  water  is  not  a  general 
type,  but  is  only  one  extreme  of  several  types.  Any  comprehensive 
theory  of  electrolytic  solutions  must  obviously  account  for  both  types. 

The  only  non-aqueous  solvent  with  regard  to  whose  solutions  we  have 
anything  like  complete  information  at  the  present  time  is  liquid  ammonia. 
This  solvent  yields  electrolytic  solutions  with  an  extremely  large  variety 
of  substances  and  we  shall  have  frequent  occasion  to  refer  to  these 
solutions  below.  At  this  point  it  will  be  sufficient  to  give  an  example  of 
the  conductance  curve  for  a  typical  salt  dissolved  in  liquid  ammonia. 
In  Table  XVIII 8  are  given  values  of  the  conductance  of  solutions  of 
potassium  nitrate  in  liquid  ammonia  at  its  boiling  point,  approximately 
—33°,  at  a  series  of  dilutions.  It  is  evident  that  these  solutions  belong 
to  the  aqueous  type,  the  conductance  increasing  throughout  with  decreas- 
ing concentration  and  approaching  a  limiting  value  at  very  low  concen- 
trations. The  limiting  value  for  potassium  nitrate  is  339.9 

TABLE  XVIII. 
CONDUCTANCE  OF  KN03  IN  NH3  AT  — 33°. 

V   324         1001         2514         6162       23060       69820          oo 

A   192.7        245.0        282.7        309.9        330.1        338.6        339. 

Y   0.567        0.720        0.831        0.912        0.972        0.995 

Solutions  of  typical  salts  in  liquid  ammonia  exhibit  a  somewhat  higher 
conductance  than  do  the  corresponding  salts  in  water,  but  it  is  evident 
that  the  ionization  of  these  salts  in  liquid  ammonia  solutions  is  consid- 
erably lower  than  in  water,  as  may  be  seen  from  Figure  3.  Ammonia 
apparently  approaches  ordinary  alcohol  and  acetone  in  its  ionizing  power. 
In  the  case  of  certain  solutions  in  liquid  ammonia,  an  intermediate  type 
of  conductance  curve  is  found.  This  is  the  case,  for  example,  with  potas- 
sium amide  whose  curve  exhibits  a  minimum.10 

A  similar,  but  in  some  respects  a  slightly  different,  case  is  found  in 
certain  of  the  cyanides,  of  which  mercuric  cyanide  and  silver  cyanide 
may  serve  as  examples.  The  conductance  values  for  solutions  of  mer- 
curic cyanide  in  ammonia  are  given  in  Table  XIX.11 

•Franklin  and  Kraus,  Am.  Chem.  J.  23,  277  (1900). 

9  Kraus  and  Bray,  J.  Am.  Chem.  Soc.  35,  1037   (1913). 

10  Franklin,  Ztachr.  f.  phj/s.  Chem.  69,  290   (1909). 
"Franklin  and  Kraus,  loc.  cit. 


ELECTROLYTIC  SOLUTIONS  IN  VARIOUS  SOLVENTS  53 

TABLE  XIX. 
CONDUCTANCE  OF  Hg(CN)2  IN  NH3  AT  —33°. 

V  1.16        3.37        5.71        21.8        33.0        55.6 

A  2.48        1.86        1.79        1.63        1.64        1.75 

The  solutions  of  this  salt  exhibit  a  conductance  curve  with  a  very  flat 
minimum,  the  curve  thus  being  similar  to  that  of  potassium  iodide  in 
methylamine.  Silver  cyanide  likewise  exhibits  a  curve  with  a  minimum. 
The  values  are  given  in  Table  XX.12 

TABLE  XX. 
CONDUCTANCE  OF  AgCN  IN  NH3  AT  — 33°. 

V 4.48      9.02     17.85    35.25    69.69     137.7    272.8    538.0     1063.0 

A  ....   15.58     15.39     14.28    13.45     12.83     12.41     12.12     12.00      12.00 

It  is  evident  from  these  values  that  the  conductance  curve  for  silver 
cyanide  has  a  very  flat  minimum  in  the  neighborhood  of  10~3  normal. 
What  is  more  striking,  however,  is  the  fact  that  the  conductance  changes 
so  little  with  the  concentration.  The  entire  change  between  10~3  normal 
and  0.5  normal  is  only  from  12.00  to  15.5  or  about  30  per  cent. 

We  see  that  solutions  in  non-aqueous  solvents  exhibit  a  great  variety 
of  properties  many  of  which  diverge  largely  from  those  of  aqueous  solu- 
tions. A  great  variety  of  liquids  are  capable  of  forming  electrolytic  solu- 
tions with  various  substances  and  many  substances  which  do  not  form 
electrolytic  solutions  when  dissolved  in  water  form  such  solutions  in 
other  solvents. 

2.  Applicability  of  the  Mass-Action  Law  to  Non-Aqueous  Solutions. 
From  a  study  of  aqueous  solutions  of  electrolytes,  the  conclusion  was 
reached  that  the  conductance  is  due  to  the  motion  of  charged  carriers 
through  these  solutions  and  that  these  charged  carriers  are  in  equilibrium 
with  the  neutral  molecules  of  the  electrolyte.  In  other  words,  the  elec- 
trolyte is  dissociated,  or  ionized,  to  use  the  accepted  term  for  this  process, 
and  the  degree  of  ionization  may  be  measured  by  means  of  the  ratio  of 
the  equivalent  conductance  of  the  solution  to  the  limiting  value  which  the 
equivalent  conductance  approaches  as  the  concentration  diminishes  in- 
definitely. If  this  hypothesis  is  correct,  then,  as  we  have  seen,  the  mass- 
action  law  should  apply,  and,  if  the  laws  of  dilute  solutions  may  be 
assumed  to  hold,  Equation  7  expresses  the  relation  between  the  con- 
ductance and  the  concentration  of  an  electrolytic  solution.  It  was  found 

u  Franklin  and  Kraus,  loc.  cit. 


54          PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

that  this  relation  is  fulfilled  in  the  case  of  aqueous  solutions  of  weak  acids 
and  bases,  but  is  not  fulfilled  in  the  case  of  solutions  of  electrolytes  which 
are  more  largely  ionized. 

It  is  at  once  apparent  that  non-aqueous  solutions  furnish  exceptions 
to  the  simple  mass-action  law,  since  we  have  here  cases  in  which  the 
conductance  increases  with  increasing  concentration,  which  result  is  not 
in  accord  with  Equation  7.  To  solve  the  problem  resulting  from  this 
discrepancy,  three  methods  of  attack  at  once  present  themselves.  In  the 
first  place,  the  ionization  may  not  be  correctly  measured  by  the  ratio 
A/A0.  Then,  again,  we  may  assume  that  the  reaction  equation  on  which 
the  calculations  are  based  is  not  correct.  Finally,  we  may  assume  that 
the  equilibrium  is  of  the  type  as  assumed,  but  the  conditions  assumed 
in  deriving  the  mass- action  law  are  not  fulfilled  in  the  solutions  in  ques- 
tion; in  other  words,  the  solutions  may  not  be  considered  as  dilute.  It 
is  of  course  impossible  to  state  on  a  priori  grounds  the  concentration  at 
which  the  deviations  from  the  laws  of  dilute  solutions  will  become  appre- 
ciable. The  only  method  that  we  have  of  attacking  this  problem  at 
present  is  to  carry  out  measurements  at  different  concentrations  and 
examine  the  change  in  the  mass-action  function  as  the  concentration  de- 
creases. If  the  fundamental  assumption  underlying  the  hypothesis  of 
Arrhenius  is  correct,  then  the  mass-action  function  should  approach  a 
definite  limiting  value  as  the  concentration  decreases. 

Let  us  examine,  therefore,  the  conductance  curves  of  the  more  dilute 
non-aqueous  solutions  in  order  to  determine  whether  the  mass-action 
function  approaches  a  definite  limiting  value.  It  is  obvious  that,  in  order 
to  calculate  the  degree  of  ionization,  the  value  of  A0  must  be  known  and 
this  value  can  be  obtained  only  by  extrapolation.  If  the  mass-action 
equation  in  its  simple  form  actually  holds,  then  it  is  possible  to  determine 
the  value  of  A0  by  a  very  simple  graphical  extrapolation.  Equation  7 
may  be  written  in  the  form: 

(8) 

It  is  obvious  that,  if  this  equation  holds,  the  reciprocal  of  the  equivalent 
conductance,  A,  is  a  linear  function  of  CA,  which  is  equal  to  the  specific 
conductance  multiplied  by  103.  In  other  words,  if  the  mass-action  law 
is  obeyed,  the  reciprocal  of  the  equivalent  conductance  and  the  specific 
conductance  are  connected  by  means  of  a  linear  equation.  If,  therefore, 
the  experimental  values  of  CA  and  of  I/A  are  plotted  in  a  system  of  rec- 
tangular co-ordinates,  the  points  will  lie  on  a  straight  line  if  the  mass- 
action  law  holds.  This  straight  line  extrapolated  to  the  axis  of  I/A 


ELECTROLYTIC  SOLUTIONS  IN  VARIOUS  SOLVENTS  55 

yields  the  value  of  A0  while,  obviously,  the  value  of  K  results  from  the 
slope  of  the  curve. 

Leaving  aside  for  the  moment  the  exact  values  of  A0,  we  may  roughly 
compare  the  variation  of  the  function  K  for  solutions  in  different  solvents. 
In  Table  XXI13  are  given  the  values  of  this  function  for  potassium 
nitrate  dissolved  in  ammonia  and  in  water  at  corresponding  degrees  of 
ionization. 

TABLE  XXI. 

VALUES  OF  K  FOR  SOLUTIONS  OF  KN03  IN  NH3  AND  H2O.  . 


57.00  0.2277  1.279 

70.00  0.197  0.9528 

85.59  0.167  0.3389 

91.66  0.1635  0.2332 

94.30  0.1699  0.1710 

It  is  at  once  apparent  that  the  variation  of  the  function  K  in  dilute  am- 
monia solutions  is  much  less  than  it  is  in  aqueous  solutions.  Indeed, 
between  the  ionization  values  of  70%  and  94%  the  value  of  the  con- 
ductance function  for  potassium  nitrate  in  ammonia  changes  only  by  a 
few  per  cent,  whereas,  in  aqueous  solutions,  this  function  increases  ap- 
proximately five  times.  Apparently,  therefore,  dilute  solutions  in  am- 
monia approach  the  mass-action  law  much  more  nearly  than  do  solutions 
of  the  same  substances  in  water. 

A  circumstance  which  greatly  facilitates  the  study  of  the  applicability 
of  the  mass-action  law  to  dilute  solutions  in  non-aqueous  solvents  is  the 
relatively  low  ionization  of  the  solutions  in  these  solvents.  In  the  case 
of  the  strong  electrolytes  in  water,  a  comparison  of  the  experimental  re- 
sults with  the  mass-action  law  is  rendered  difficult  by  the  high  ionization 
of  these  salts.  Since  the  expression  1  —  y,  the  value  of  the  un-ionized 
fraction,  appears  in  the  denominator  of  the  mass-action  expression,  and 
since  y  is  very  nearly  unity,  it  follows  that  the  equivalent  conductance 
must  be  determined  with  a  high  degree  of  precision  in  order  to  determine 
the  applicability  of  the  mass-action  function.  It  is  only  in  the  case  of 
potassium  chloride  that  sufficiently  precise  data  are  at  hand  to  make  a 
study  of  this  kind  possible  in  aqueous  solutions,  and  even  in  this  case  the 
results  of  such  a  comparison  remain  uncertain. 

Only  a  small  portion  of  the  data  relating  to  the  conductance  of  non- 
aqueous  solutions  has  sufficient  precision  to  make  a  comparison  with  the 
consequences  of  the  mass-action  law  possible.  It  is  only  in  the  case  of 

u  Franklin  and  Kraus,  Am.  Chem.  J.  £3f  299  (1900). 


56       PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

solutions  in  liquid  ammonia  that  we  have  such  data  relating  to  a  large 
number  of  electrolytes.  Kraus  and  Bray  14  have  examined  the  conduct- 
ance of  ammonia  solutions  from  this  point  of  view.  In  Figures  4  and  5 
are  plotted  values  of  the  reciprocal  of  the  equivalent  conductance  as 


/V3K) 


/V330 


JL&, 


2.5 


3.0 


7.5 


10.0 
tooo(cA) 


12.5 


15.0 


17.5 


FIG.  4.    Showing  Approach  of  Dilute  Solutions  in  Liquid  NH3  to  the 
Mass-Action  Law. 

ordinates  against  values  of  the  specific  conductance  as  abscissas.  In 
Figure  4  the  symbol  of  the  electrolyte  is  shown  in  the  figure,  while  in 
Figure  5  the  curves  in  order  from  1  to  7  are  for:  1,  thiobenzamide ;  2, 
orthomethoxybenzenesulphonamide;  3,  paramethoxybenzenesulphona- 


"Kraus  and  Bray,  J.  Am.  Chem.  Soc.  35,  1315  (1913). 


ELECTROLYTIC  SOLUTIONS  IN  VARIOUS  SOLVENTS 


57 


mide;  4,  metamethoxybenzenesulphonamide;  5,  nitromethane;  6,  sodium- 
nitromethane;  and  7,  orthonitrophenol.  Examining  the  figure  for  the 
typical  salts,  it  will  be  observed  that  in  the  case  of  silver  iodide,  am- 
monium chloride,  potassium  nitrate,  and  ammonium  nitrate  the  curves 


-Afi- 


A.-JA4 


ff  0.76X10*, 


KO  90X10* 


2.5 


5-0 


2-5 


12.5 


150 


175 


20.O 


IO.O 

ioo(cA) 

FIG.  5.    Showing  Approach  of  Dilute  Solutions  of  Organic  Electrolytes  in  NHs  to 

the  Mass-Action  Law. 

in  dilute  solution  approach  a  straight  line.  In  the  case  of  ammonium 
bromide  and  potassium  iodide  the  number  of  points  is  not  sufficient  to 
actually  determine  the  form  of  the  curve  in  dilute  solutions.  In  the  case 
of  other  salts,  the  figures  of  which  are  not  shown  here,  similar  results 
were  obtained;  that  is,  in  those  cases  where  sufficient  data  are  available 
at  low  concentrations,  the  points  approximate  a  straight  line  and  this 


58          PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

is  the  more  true  the  more  consistent  the  data  are  among  themselves.  In 
the  case  of  the  seven  electrolytes  in  Figure  5,  the  correspondence  with 
the  mass-action  law  is  much  more  certain.  One  reason  for  the  better 
agreement  in  the  case  of  these  electrolytes  is  their  lower  ionization,  as 
a  result  of  which  errors  in  the  value  of  the  equivalent  conductance  pro- 
duce a  smaller  variation  in  the  mass-action  constant.  Moreover,  in  these 
cases  the  mass-action  law  appears  to  apply  to  greater  total  salt  concen- 
trations. In  view  of  the  fact  that  the  original  experimental  results  are 
independent  of  any  considerations  as  to  the  applicability  of  the  mass- 
action  law,  the  conclusion  appears  justified  that  in  the  case  of  solutions 
in  liquid  ammonia  the  mass-action  function  approaches  a  limiting  value 
at  low  concentrations. 

The  total  salt  concentration  at  which  the  deviations  from  the  simple 
mass-action  law  become  appreciable  is  the  lower,  the  greater  the  ioniza- 
tion of  the  electrolyte.  In  this  respect  solutions  in  ammonia  resemble 
solutions  of  the  acids  and  bases  in  water.  The  lower  the  ionization  of 
an  acid  or  a  base  in  water,  the  higher  the  concentration  up  to  which  the 
mass-action  law  appears  to  hold.  From  an  examination  of  their  results, 
Kraus  and  Bray  drew  the  conclusion,  however,  that  the  deviations  from 
the  mass-action  law  become  appreciable  for  different  electrolytes  in 
ammonia  solution  at  about  the  same  ion  concentration.  They  found 
that  the  mass-action  function  for  a  number  of  electrolytes  was  increased 
over  the  limiting  value  by  5%  at  ion  concentrations  lying  in  the  neigh- 
borhood of  1  X  10"4  N.  It  is,  however,  apparent  that  in  certain  cases  the 
ion  concentration  is  considerably  greater  and  in  other  cases  considerably 
lower  than  this  value.  So,  for  example,  in  the  case  of  potassium  amide 
this  concentration  is  2.76  X  10~*,  while  in  that  of  trinitraniline  it  is 
0.22  X  10-4. 

We  may  now  consider  the  values  of  the  mass-action  constant  for 
different  electrolytes  in  ammonia  solution.  The  values  for  the  inorganic 
electrolytes  are  given  in  Table  XXII 15  (see  opposite  page) . 

It  is  apparent,  in  the  first  place,  that  the  values  of  the  mass-action  con- 
stant for  the  different  inorganic  electrolytes  differ  considerably.  The  ex- 
treme values  lie  between  0.056  X  10~4  for  sodium  amide  and  42  X  10'4 
for  potassium  iodide.  The  greater  number  of  the  salts,  however,  have 
ionization  constants  lying  between  21  X  10~4  and  28  X  10~4.  This  varia- 
tion of  the  ionization  constants  for  different  inorganic  electrolytes  in  am- 
monia is  in  striking  contrast  with  the  nearly  identical  ionization  of  the 
same  electrolytes  in  water.  It  should  be  borne  in  mind,  however,  that  in 
aqueous  solution  the  degree  of  ionization  is  so  high,  in  any  case,  that  dif- 

18  Kraus  and  Bray,  loc.  cit. 


ELECTROLYTIC  SOLUTIONS  IN  VARIOUS  SOLVENTS  59 

TABLE  XXII. 
VALUES  OF  K  AND  A0  FOR  DIFFERENT  ELECTROLYTES  IN  NH3  AT  —  33°. 

Salt  WK  A0 

NaNH2    0.056  263 

KNH2    1.20  301 

Agl   2.90  287 

NH4C1  12.0  310 

NaCl 14.5  309 

KN03  15.5  339 

KBr  21.0  340 

T1N03 21.0  323 

NaBr03    23.0  378 

NaN03  23.0  301 

NH4Br   23.0  303 

LiN03 26.0  283 

NaBr  27.0  302 

Nal    28.0  301 

AgN03    28.0  287 

NH4N03   28.0  302 

KI  42.0  339 

ferences  in  the  ionization  values  of  the  different  electrolytes  are  neces- 
sarily very  small.  Nevertheless,  we  must  conclude  that  the  ionization 
values  of  typical  salts  in  water  are  much  more  nearly  the^same  in  that 
solvent  than  they  are  in  ammonia  or  in  any  other  solvent  for  which 
reliable  data  are  available.  The  order  of  the  ionization  constants  does  not 
appear  to  bear  any  relation  to  the  constitution  of  the  electrolytes.  So 
ammonium  chloride  has  an  ionization  constant  of  12  X  10"*  and  am- 
monium nitrate  of  28  X  10~4,  while  silver  iodide  has  an  ionization  con- 
stant of  2.9  X  10"*  and  silver  nitrate  28  X  10"*.  Sodium  nitrate  has  a 
greater  ionization  constant  than  potassium  nitrate,  while  sodium  iodide 
has  a  smaller  ionization  constant  than  potassium  iodide. 

The  constants  for  sodium  and  potassium  amides  are  of  interest  owing 
to  the  fact  that  these  substances  are  bases  in  liquid  ammonia  solution. 
Apparently  these  substances  are  relatively  weak  bases  when  compared 
with  the  typical  salts  in  ammonia  or  when  compared  with  corresponding 
bases  in  water.  Indeed,  it  is  apparent  that  all  electrolytes  in  ammonia 
solution  have  comparatively  small  ionization  constants.  For  example, 
the  ionization  constant  of  acetic  acid  in  water  is  0.182  X  10"*.  The 
ionization  constant  of  this  acid,  therefore,  is  approximately  three  times 
that  of  sodium  amide  and  1/7  that  of  potassium  amide. 

The  ionization  constants  for  a  number  of  organic  electrolytes  in  liquid 


60          PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

ammonia  are  given  in  Table  XXIII.16    Here,  again,  we  find  a  large  varia- 
tion in  the  value  of  the  ionization  constant  for  different  electrolytes. 

TABLE  XXIII. 
VALUES  OF  K  AND  OF  A0  FOR  ORGANIC  ELECTROLYTES  IN  NH3  AT  — 33°. 

Salt  104#  A0 

Cyanacetamide  0.045  260 

Thiobenzamide   0.40  204 

Orthomethoxybenzenesulphonamide 0.40  208 

Paramethoxybenzenesulphonamide    0.50  208 

Nitromethane    0.53  278 

Sodiumnitromethane    0.78  278 

Benzenesulphonamide    1.39  208 

Metamethoxybenzenesulphonamide    1.81  208 

Orthonitrophenol    3.90  246 

Methylnitramine  8.4  256 

Phthalimide    8.7  248 

Benzoicsulphinide    12.0  206 

Metanitrobenzenesulphonamide    12.5  231 

Potassiummetanitrobenzenesulphonate   15.0  275 

Nitrourethaneammonium    21.6  262 

Trinitrobenzene   30.0  234 

Trinitraniline  30.0  234 

The  strongest  "of  these,  trinitraniline  and  trinitrobenzene,  have  ionization 
constants  as  great,  or  greater,  than  those  of  typical  salts  in  ammonia. 
On  the  other  hand,  cyanacetamide  has  an  ionization  constant  of  only 
0.045  X  10~4.  Cyanacetamide,  therefore,  is  a  weaker  acid  in  ammonia 
solution  than  acetic  acid  is  in  water,  and  of  course  a  much  weaker  acid 
than  cyanacetic  acid  in  water.  In  other  respects,  as  regards  the  relation 
of  the  ionization  constants  of  these  electrolytes  to  their  constitution,  we 
find  relations  similar  to  those  in  aqueous  solutions.  The  introduction  of 
strongly  electronegative  groups  into  the  negative  constituent  increases 
the  value  of  the  ionization  constant.  It  will  be  observed  that  many  of 
the  organic  substances  which  act  as  electrolytes  in  ammonia  solution  are 
not  electrolytes  in  water.  This  is  true  of  nearly  all  the  acid  amides  and 
of  such  compounds  as  trinitrobenzene.  The  positive  ion,  in  the  case  of 
the  acid  amides,  as  indeed  in  the  case  of  all  the  acids  in  ammonia  solu- 
tion, is  presumably  the  ammonium  ion.17 

Having  seen  that  the  mass-action  law  applies  to  dilute  solutions  of 
practically  all  electrolytes  in  ammonia,  we  may  inquire  whether  the  same 

"  Kraus  and  Bray,  loc.  cit. 
»  Ibid.,  loc.  cit.,  p.  1357. 


ELECTROLYTIC  SOLUTIONS  IN  VARIOUS  SOLVENTS 


61 


is  true  of  solutions  in  other  non-aqueous  solvents.  In  Table  XXIV18 
are  given  values  of  the  mass-action  constants  for  sodium  iodide  in  a  num- 
ber of  different  solvents.  In  Figure  6  are  plotted  values  of  the  reciprocal 
conductance  against  those  of  the  specific  conductance  for  these  solutions. 


A.-M 


A,-** 


130 


.0* 


goo 


3  4  5  6  7  S 

ioo(cA)  [for  Isoamylalcohol  iooo(cA)J 

FIG.  6.  Showing  how  Solutions  of  Binary  Electrolytes  in  Different  Solvents  Approach 
the  Mass-Action  Relation  at  Low  Concentrations. 

An  examination  of  the  figure  shows  that  in  all  cases  the  conductance 
curves  approach  a  linear  relation  in  the  more  dilute  solutions.  We  may 
conclude,  therefore,  that  in  the  case  of  non-aqueous  solvents,  in  general, 
the  mass-action  law  is  approached  as  a  limiting  form  at  low  concentra- 
tions. 


"Kraus  and  Bray,  loc.  cit. 


62          PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

TABLE  XXIV. 

VALUES  OF  K  AND  OF  A0  FOR  ELECTROLYTES  IN  DIFFERENT  SOLVENTS. 

Solvent                               Solute  Temp.  °C.  K  X 10*  A0 

Benzonitrile    Nal  25°  55.0  49.0 

Epichlorhydrin (C2H5)4NI  25°  48.5  62.1 

Propylalcohol  Nal  18°  45.0  20.6 

Acetone  Nal  18°  30.0  167.0 

Acetophenone Nal  25°  34.0  35.6 

Methylethylketone Nal  25°  23.0  139.0 

Pyridine  Nal  18°  13.0  61.0 

Isobutylalcohol  Nal  25°  12.0  13.7 

Acetoaceticester    NaSCN  18°  9.5  32.1 

Isoamylalcohol   Nal  25°  3.9  9.2 

Ethylenechloride   (C3H7)4NI  25°  1.45  66.7 

The  mass-action  constant  varies  with  the  nature  of  the  solvent.  The 
greatest  value  is  that  for  benzonitrile,  which  is  55  X  10~4,  and  the  smallest 
that  for  ethylenechloride,  which  is  1.45  X  10'4.  The  change  in  the  value 
of  the  ionization  constant  among  the  alcohols  is  of  particular  interest  in 
view  of  their  relation  to  water.  The  constant  for  solutions  in  propyl 
alcohol  is  45  X  10~4,  in  isobutylalcohol  12  X  10~4,  and  in  isoamylalcohol 
3.9  X  10~4.  It  is  evident  that,  as  the  substituting  hydrocarbon  group 
becomes  more  complex,  the  ionization  constant  decreases.  These  results 
also  have  a  bearing  on  the  probable  behavior  of  aqueous  solutions.  The 
properties  of  solutions  in  the  lower  alcohols  differ  only  inconsiderably 
from  those  of  aqueous  solutions.  It  seems  probable,  therefore,  that  in 
going  from  water  through  the  lower  alcohols  to  the  higher  alcohols  the 
change  in  the  phenomenon  underlying  the  ionization  process  undergoes 
an  alteration  in  degree  rather  than  in  kind.  It  might  be  concluded, 
therefore,  that  in  aqueous  solutions,  also,  the  mass-action  law  is  ap- 
proached as  a  limiting  form.  This  question,  however,  will  be  discussed 
at  somewhat  greater  length  in  a  succeeding  chapter. 

A  considerable  number  of  data  are  available  on  the  conductance  of 
dilute  solutions  in  acetone.  In  the  following  table  are  given  values  of 
the  mass-action  constant  and  the  limiting  values  of  the  equivalent  con- 
ductance for  a  series  of  electrolytes  in  this  solvent. 

TABLE  XXV. 

VALUES  OF  K  AND  OF  A0  FOR  DIFFERENT  ELECTROLYTES  IN  ACETONE  AT  18°. 
Solute  104  K  A0 

KI    51.0  156 

Nal 39.0  156 

Lil 31.0  154 


ELECTROLYTIC  SOLUTIONS  IN  VARIOUS  SOLVENTS  63 

TABLE  XXV.— Continued. 
Solute  104K  A0 

NH4I  15.0  159 

KSCN   31.0  169 

LiSCN    18.0  167 

NH4SCN   8.3  172 

KBr  16.0  156 

NaBr  13.0  156 

LiBr   5.7  154 

NH4Br   2.3  159 

LiN03    2.6  125 

AgN03   0.28  100 

LiCl  0.94  154 

From  an  examination  of  this  table  it  is  obvious  that  the  ionization  con- 
stants of  typical  salts  in  acetone  vary  within  very  wide  limits.  So,  the 
ionization  constant  for  silver  nitrate  is  0.28  X  10'*,  whereas  that  for 
potassium  iodide  is  51.0  X  10"*.  More  remarkable  still  is  the  regularity 
in  the  variation  of  the  constants  as  a  function  of  the  constitution  of  the 
electrolyte.  The  ionization  constants  of  the  iodides  diminish  in  the  order 
potassium,  sodium,  lithium,  ammonium.  The  same  order  holds  in  the 
case  of  all  other  salts,  namely  the  sulfocyanates,  bromides,  and  nitrates. 
On  the  other  hand,  the  ionization  constants  of  salts  with  a  common  posi- 
tive ion  vary  in  the  order:  iodides,  sulfocyanates,  bromides,  nitrates, 
chlorides.  This  order  holds  true  in  every  case.  It  appears,  therefore, 
that  the  ionization  constant  K  is  an  additive  function  of  the  constituent 
ions  of  the  electrolytes.  This  is  the  only  solvent  for  which  such  a  rela- 
tion appears  to  hold  true.  What  the  significance  of  this  may  be  is  at 
present  uncertain.  It  is  important,  however,  to  observe  that  the  ioniza- 
tion of  different  typical  salts  in  acetone  varies  within  extremely  wide 
limits.  The  similarity  in  the  behavior  of  strong  electrolytes  in  aqueous 
solutions,  as  regards  their  ionization,  is  therefore  not  to  be  considered  as 
a  property  which  may  be  ascribed  primarily  to  the  electrolytes  them- 
selves, but  rather  one  in  which  the  solvent  itself  appears  as  the  chief 
factor. 

3.  Comparison  of  the  Ion  Conductances  in  Different  Solvents.  If 
the  values  of  A0  are  known  and  if  the  transference  numbers  of  the 
electrolytes  are  known,  then  the  values  of  the  ion  conductances  may  be 
determined.  However,  before  proceeding  to  a  comparison  of  the  values 
of  the  ion  conductances  in  different  solvents,  it  will  be  well  to  point  out 
that  the  value  of  A0  is  dependent  upon  the  form  of  the  extrapolation 
function  which  must  be  assumed.  Only  in  the  case  of  solutions  which 


64          PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

approach  the  mass-action  law  as  a  limiting  form  may  we  be  reasonably 
certain  that  the  extrapolated  value  of  A0  is  correct.  In  other  cases, 
therefore,  the  limiting  conductance  values  are  more  or  less  arbitrary.  In 
a  subsequent  chapter  this  question  will  be  discussed  somewhat  more  at 
length.  For  the  present  we  shall  assume  that  the  A0  values  obtained  by 
the  ordinary  methods  of  extrapolation  are  approximately  correct. 

The  values  of  the  equivalent  conductances  of  the  different  electrolytes 
in  ammonia  and  water  have  been  given  in  Tables  III,  XXII  and  XXIII. 
In  comparing  the  conductances  in  the  two  solvents,  however,  it  is  pre- 
ferable to  compare  the  conductance  of  the  individual  ions,  rather  than 
that  of  the  sum  of  the  ions  of  any  given  electrolyte.  Before  proceeding 
further,  therefore,  we  shall  resolve  these  values  of  the  conductance  for 
the  various  electrolytes  into  two  parts,  namely  the  conductance  of  the 
positive  and  of  the  negative  ion  respectively.  In  order  that  this  may  be 
done,  it  is  necessary  that  the  transference  number  of  at  least  one  elec- 
trolyte shall  be  known.  In  the  case  of  ammonia  solutions  the  transfer- 
ence numbers  of  a  considerable  number  of  electrolytes  have  been  deter- 
mined by  Franklin  and  Cady.19  With  the  aid  of  their  data,  the  follow- 
ing values  of  the  equivalent  conductance  of  the  typical  inorganic  ions 
have  been  calculated.20  For  the  sake  of  comparison,  the  ion  conduct- 
ances of  the  same  ions  in  water  at  18°  are  given  as  well  as  the  ratio  of 
the  ion  conductances  in  ammonia  and  in  water. 

TABLE  XXVI. 
ION  CONDUCTANCES  IN  AMMONIA  AND  IN  WATER. 

Ion  In  NH3  In  H20        ANH  /AR  Q 

Positive    Li+    112  33.3  3.36 

Ag+    116  54.0  2.15 

Na+   130  43.4  3.00 

NH4+    131  64.7  2.03 

T1+   152  65.9  2.31 

K+   168  64.5  2.61 

Negative  Br03-   148  47.6  3.11 

N03-  171  61.8  2.77 

I-  171  66.6  2.57 

Br- 172  67.7  2.54 

Cl-  179  65.5  2.73 

NH2-  133 

"Franklin  and  Cady,  J.  Am.  Chem.  Soc.  26,  499   (1904). 
10  Kraus  and  Bray,  loc.  cit. 


ELECTROLYTIC  SOLUTIONS  IN  VARIOUS  SOLVENTS  65 

It  will  be  observed  that  the  ion  conductances  in  ammonia  and  in 
water  do  not  stand  in  a  fixed  ratio.  For  example,  for  the  silver  ion,  the 
ion  conductance  in  ammonia  is  2.15  times  that  in  water,  whereas  for 
the  lithium  ion  the  conductance  in  ammonia  is  3.36  times  that  in  water. 
Similarly,  the  conductance  of  the  bromide  ion  in  ammonia  is  2.54  times 
that  itf  water,  while  the  conductance  of  the  bromate  ion  is  3.11  times 
that  in  water.  We  may  naturally  inquire  as  to  what  are  the  factors 
upon  which  depends  the  conductance  of  different  ions  in  different  solvents. 

If  the  current  is  carried  through  a  solution  by  the  translation  of 
charged  particles  of  molecular  dimensions,  then  we  should  expect  the 
speed  of  these  particles  to  be  a  function  of  the  viscosity  of  the  medium 
through  which  they  move.  It  might  be  assumed,  for  example,  that  the 
conductance  is  proportional  to  the  reciprocal  of  the  viscosity,  or  to  the 
fluidity  of  the  solvent.  The  viscosity  of  water  at  18°  is  10.63  X  10"3  and 
that  of  ammonia  is  2.558  X  10'3  at  its  boiling  point.  Consequently  the 
fluidity  of  ammonia  is  4.15  times  as  great  as  that  of  water.  If  the  con- 
ductance of  the  ions  were  directly  proportional  to  the  fluidity  of  the 
solvent,  then  the  conductance  of  all  ions  in  ammonia  should  be  4.15  times 
as  great  as  that  of  the  same  ions  in  water.  We  see,  however,  that  while 
the  conductance  of  the  various  ions  in  ammonia  is  markedly  greater 
than  that  in  water,  nevertheless  the  ratio  of  the  ion  conductances  in  the 
two  solvents  is  in  all  cases  smaller  than  this  value.  Furthermore,  the 
effect  is  one  specific  with  respect  to  the  individual  ions.  For  example, 
for  the  sodium  ion,  the  value  is  3.0,  while  for  the  lithium  ion  it  is  3.36. 
It  is  noticeable  that  the  ratio  for  the  ions  increases  in  the  order:  am- 
monium, potassium,  sodium,  lithium.  In  other  words,  in  ammonia  the 
lithium  ion  possesses  a  relatively  much  higher  conductance  with  respect 
to  water  than  does  the  ammonium  ion. 

The  same  general  relations  hold  in  the  case  of  the  negative  ions.  The 
conductance  of  the  bromate  ion  in  ammonia  is  3.11  times  that  in  water, 
whereas  that  of  the  bromide  ion  is  only  2.54  times  that  in  water.  On 
the  whole,  the  ion  conductances  in  ammonia  vary  less  than  they  do  in 
water.  The  extreme  variation  in  the  case  of  ammonia  solutions  is  from 
112,  for  the  lithium  ion,  to  168,  for  the  potassium  ion,  or  a  ratio  of  1.5, 
whereas  in  the  case  of  aqueous  solutions  the  extreme  variation  is  from 
33.3,  for  the  lithium  ion,  to  65.9,  for  the  thallous  ion,  or  a  ratio  of  1.98. 
For  the  negative  ions  in  ammonia  solution  the  extreme  ratio  is  1.21, 
whereas  for  aqueous  solutions  it  is  1.37.  In  general,  however,  the  order 
of  ionic  conductances  in  the  two  solvents  is  the  same.  With  a  few  ex- 
ceptions, ions  which  move  very  slowly  in  water  also  move  very  slowly 
in  ammonia. 


66          PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

It  is  evident  that  the  conductance  of  an  ion  is  a  function  of  the  con- 
stitution of  the  solvent  as  well  as  of  that  of  the  ion  itself.  In  this  con- 
nection it  should  be  observed  that  a  given  electrolyte  dissolved  in  two 
different  solvents  does  not  necessarily  yield  the  same  ions.  In  other 
words,  complexes  may  be  formed  between  the  ions  and  the  solvent  proper- 
ties of  which  will  depend  upon  the  nature  of  the  solvent.  It  -is  well 
known  that  certain  ions  tend  to  form  complexes  with  certain  solvents.  For 
example,  the  silver  ion  forms  a  complex  with  ammonia  even  in  aqueous 
solutions.  It  may  be  assumed,  therefore,  that  the  silver  ion  has  a  great 
tendency  to  form  complexes  with  ammonia.  The  cause  for  the  relatively 
low  value  of  the  conductance  of  the  silver  ion  in  ammonia  may  be 
ascribed  to  the  formation  of  a  relatively  large  complex  silver-ammonia 
ion  in  ammonia  solution.  Similarly,  those  ions  whose  salts  show  a 
marked  tendency  to  form  complexes  with  water,  which,  for  example, 
give  stable  crystalline  hydrates,  show  a  relatively  higher  speed  in  am- 
monia than  in  water.  Thus,  the  speed  of  the  lithium  ion  in  ammonia  is 
relatively  much  greater  with  respect  to  its  speed  in  water  than  is  that 
of  the  potassium  ion.  We  may  therefore  conclude  that  the  lithium  ion 
is  relatively  less  complex  in  ammonia  than  it  is  in  water. 


Chapter  IV. 
Form  of  the  Conductance  Function. 

1.  The  Functional  Relation  between  Conductance  and  Concentra- 
tion. If  an  equilibrium  exists  between  the  ions  and  the  un-ionized  mole- 
cules in  a  solution,  then  the  relation  between  the  conductance  and  the 
concentration  is  expressed  by  Equation  7,  which  follows  from  the  mass- 
action  law.  We  have  seen  that  this  equation  is  fulfilled  in  solutions  of 
weak  electrolytes  in  water  and  that  it  is  approached  as  a  limiting  form 
in  solutions  of  strong  electrolytes  in  non-aqueous  solvents.  This  equa- 
tion is  the  only  one  so  far  suggested  to  account  for  the  relation  between 
the  conductance  and  the  concentration  which  has  a  substantial  theoretical 
foundation  for  its  support.  At  higher  concentrations,  in  the  case  of  the 
stronger  electrolytes,  both  in  water  and  in  non-aqueous  solvents,  the 
simple  form  of  the  mass-action  law  no  longer  holds.  Except  at  very 
high  concentrations,  where  viscosity  effects  become  pronounced,  the  con- 
ductance in  all  cases  varies  in  such  a  way  that  the  value  of  the  mass- 
action  function  increases  with  increasing  concentration.  If  the  reciprocal 
of  the  equivalent  conductance  is  plotted  against  the  specific  conductance, 
then,  in  the  case  of  strong  electrolytes,  it  is  found  that  the  experimental 
curve  is  concave  toward  the  axis  of  specific  conductances. 

We  have  seen  that  in  different  solvents  the  conductance  curve,  as  a 
function  of  the  concentration,  varies  greatly  in  form,  and  the  conclusion 
might  be  drawn  that  the  process  involved  in  these  solutions  is  entirely 
different  in  character.  Since  the  form  of  the  conductance  function  in 
the  case  of  the  concentrated  solutions  is  thus  far  not  determinable  from 
theoretical  considerations,  various  attempts  have  been  made  to  deter- 
mine empirical  functions  which  should  express  the  conductance  in  terms 
of  the  concentration.  In  the  case  of  aqueous  solutions  the  equation  of 
Storch  a  appears  to  apply  over  a  considerable  concentration  range.  This 
equation  may  be  written  in  the  form: 


where  D  and  m  are  constants.    This  equation  applies  remarkably  well 
in  the  case  of  aqueous  solutions,  even  up  to  high  concentrations.    It  will 

'Storcb,  Ztschr.  /.  pJiyg.  Chem.  19,  13   (1896). 

67 


68 


PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 


be  observed  that  in  this  equation  the  mass-action  function  K'  is  expressed 
as  a  function  of  the  ion  concentration  raised  to  the  ra'th  power.  The 
equation  may  be  tested  very  simply  by  graphical  methods.  It  may  be 
written  in  the  form: 

(10)  (2  —  m)  log  (CY)  —  log  [C  (1  —  Y)  ]  =  log  D. 

If,  therefore,  we  plot  the  logarithms  of  (7(1— y)  against  the  logarithms 
of  the  ion  concentrations  Cy  or  the  specific  conductances,  the  experi- 
mental points  should  lie  on  a  straight  line,  provided  the  equation  holds. 
This  method  of  treatment  was  first  proposed  by  Bancroft2  and  has 
proved  extremely  useful  in  determining  the  behavior  of  very  concen- 
trated solutions.  In  Figure  7  are  shown  the  curves  for  potassium  chloride 
and  potassium  nitrate  in  water  at  18°.  It  will  be  observed  that  the  points 
lie  very  nearly  on  a  straight  line. 


0.0 


5.0 


2.0 


0.0 


3.0 

LogC  (1  —  Y). 
FIG.  7.    Plot  of  Storch  Equation  for  Aqueous  Solutions  of  Binary  Electrolytes. 

It  is  evident,  however,  that  an  equation  of  this  type  cannot  apply 
generally,  since  it  does  not  approach  the  mass-action  expression  as  a 
limiting  form.  As  we  have  seen,  dilute  solutions  in  non-aqueous  solvents 
approach  the  mass-action  function  at  low  concentrations.  It  has  there- 
fore been  proposed  3  to  express  the  relation  between  the  conductance  and 
the  concentration  by  means  of  the  equation: 


(ii) 


K'= 


0(1  — 


2  Bancroft,  Ztschr.  f.  phys.  Chem.  SI,  188   (1899). 

•Kraus,  Proc.  Am.  Chem.  Soc.  1909,  p.  15;  Bray,  Science  35,  433  (1912)  ;  Trans.  Am. 
Electro-Ch.  Soc.  21,  143  (1912)  ;  MacDougall,  J.  Am.  Chem.  Soc.  34,  855  (1912)  ;  Kraus 
and  Bray,  J.  Am.  Ohem.  Soc.  35,  1315  (1913).  Somewhat  similar  four-constant  equations 


FORM  OF  THE  CONDUCTANCE  FUNCTION  69 

In  this  equation  y  is  written  for  the  ratio  -r-  for  the  sake  of  brevity.    An 

A0 

inspection  of  this  equation  shows  that  at  low  concentrations  the  first 
term  of  the  right-hand  member,  involving  the  ion  concentration  Cy,  will 
diminish  as  the  concentration  decreases,  and  will  ultimately  become  neg- 
ligible in  comparison  with  the  constant  K.  On  the  other  hand,  at  higher 
concentrations,  the  constant  K  will  become  negligible  in  comparison  with 
the  term  involving  the  ion  concentration.  In  other  words,  at  high  con- 
centrations this  equation  approaches  the  Storch  Equation  9  as  a  limiting 
•form. 

Obviously,  this  equation  involves  the  four  constants  A0,  K,  D  and  ra. 
These  constants  may  in  most  cases  be  determined  readily  by  graphical 
means.  If  conductance  data  are  available  at  very  low  concentrations, 
the  second  term  of  the  right-hand  member  may  be  neglected,  in  which 
case  the  reciprocal  of  the  equivalent  conductance  becomes  a  linear  func- 
tion of  the  ion  concentration;  that  is,  the  equation  degenerates  into  the 
form  of  Equation  7.  The  value  of  A0  and  of  K  may  therefore  be  de- 
termined with  a  considerable  degree  of  precision  from  this  plot.  Hav- 
ing determined  these  two  constants,  the  values  of  m  and  D  may  be  de- 
termined from  data  at  higher  concentrations.  At  very  high  concentra- 
tions K  may  be  neglected  and  from  a  plot  of  Equation  10,  which  is 
linear  if  the  equation  holds,  the  values  of  ra  and  D  may  be  determined. 
In  case  the  constant  K  is  not  negligible  at  higher  concentrations,  it  is 
necessary  to  take  this  into  account.  This  may  be  done  by  means  of  a 
second  approximation.  It  is  seen  from  Equation  11  that  the  mass-action 

Cv* 
function  K'  =     _     is  a  linear  function  of  the  ion  concentration  raised 

to  the  ra'th  power.  If  the  value  of  ra  in  the  more  concentrated  solutions, 
as  determined  by  the  first  approximation,  is  correct,  then  the  values  of 
K  and  D  may  be  corrected  by  means  of  a  plot  of  K'  against  (Cy)m. 
The  value  of  K  is  then  determined  by  extrapolating  to  the  concentration 
zero  and  the  value  of  D  is  determined  from  the  slope  of  the  line.  The 
values  of  the  constants  having  been  determined,  it  is  possible  to  calcu- 
late the  conductance  of  a  given  electrolyte  at  any  desired  concentration 
and  to  compare  the  calculated  with  the  experimental  values. 

In  Figure  8  is  shown  a  plot  of  the  reciprocal  of  the  equivalent  con- 
ductance against  the  specific  conductance  or  ion  concentration  for  solu- 
tions of  potassium  amide  in  liquid  ammonia.4  This  plot  yields  for  A0 

have  been  proposed  by  Bates  (J.  Am.  Chem.  Soc.  37.  1431   (1915))   and  bv  de 
(Medd.  K.  Vet.  Akad's  Nobelinstitut,  Vol.  3,  Nos.  2  and  11    (1914))       While 


equations  represent  the  course  of  the  conductance  curve  fairly  well  in  the  case  of  aaueoua 
solutions,  they  are  not  generally  applicable  to  non-aqueous  solutions 
«  Franklin,  Ztschr.  f.  phys.  Chem.  69,  290 


70         PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

the  value  301  and  for  K  the  value  1.26  X  10'4.5  That  is,  the  straight 
line  drawn  corresponding  to  this  slope  passes  through  the  points  in  the 
more  dilute  solutions. 


o 

0.0 


2.5  5.0  7.5  10  12.5  15 

100  (CA). 
FIG.  8.    A0  —  K  Plot  for  KNH2  in  NH3. 


17-5 


Having  determined  the  preliminary  values  of  K  and  of  A0,  we  may 
plot  the  values  of  the  logarithm  of  K'— K  against  the  logarithm  of  Cy. 
The  plot  for  this  function  is  shown  in  Figure  9,  where  it  will  be  observed 


2.0 

5-0 
3* 

£| 

|g 

/ 

D-0093 

|g 

^ 

P 

o           3'5             2.0            2.5            T.o            1.5             o. 

Log  tar) 

FIG.  9.    M  —  D  Plot  lor  KNH2  in  NH3. 

that  the  points  lie  upon  a  straight  line  well  within  the  limits  of  experi- 
mental error.  This  plot  yields  a  value  of  D  =  0.095  and  ra  =  1.18. 
Finally,  in  order  to  obtain  a  more  precise  value  of  K,  values  of  K.'  are 

•Kraus  and  Bray,  loc.  cit. 


FORM  OF  THE  CONDUCTANCE  FUNCTION 


71 


plotted  against  the  values  of  the  ion  concentration  to  the  power  1.18. 
This  plot  is  shown  in  Figure  10.  The  value  for  D  in  this  case  is  not 
altered  from  that  originally  determined,  but  the  value  of  K  is  altered 
from  1.26  to  1.20. 

It  will  be  observed  that,  throughout,  the  points  lie  upon  a  straight 
line  within  the  limits  of  experimental  error.    The  equation  connecting 


K-UOXMT* 


•0.0 


2.5 


5.0 


7-5 


12.5 


15 


17.5 


20.0 


FIG.  10.    K—  D  Plot  for  KNH,  in  NH,. 

the  equivalent  conductance  with  the  concentration  for  solutions  of  potas- 
sium amide  in  liquid  ammonia  is,  therefore: 


K'  = 


n 

yl*  —  Y/ 


=  0.095  (Cy)118  +  1.20  X  10"4 


where  y=_. 

The  calculated  values  are  compared  with  the  experimental  values  in 
Figure  11,  where  the  equivalent  conductances  are  plotted  as  ordinates 
against  the  logarithms  of  the  concentrations  as  abscissas.  It  will  be  ob- 
served that  the  calculated  curve  corresponds  with  the  experimental  curve 
up  to  a  concentration  of  approximately  2  normal.  Beyond  this  concen- 
tration the  experimental  curve  departs  rapidly  from  the  calculated  curve. 
As  we  shall  see  presently,  at  higher  concentrations,  the  viscosity  of  the 
solutions  increases  very  largely  and  it  is  therefore  not  possible  to  test 
the  applicability  of  the  equation  at  these  concentrations. 

It  becomes  a  matter  of  interest  to  determine  whether  an  equation  of 


72 


PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 


this  type  is  generally  applicable  to  solutions  of  electrolytes  in  various 
solvents.  Since  a  larger  amount  of  experimental  material  is  available 
for  solutions  in  liquid  ammonia  than  for  solutions  in  any  other  solvent, 
we  may  consider  solutions  in  this  solvent  first.  Since  the  more  dilute 
solutions  have  already  been  considered  and  found  to  conform  to  the 


280 


240 


<200 


160 


120 


80 


40 


\ 


\ 


5-0 


1.0 


0.0 


1.0 


40  3.0  2.0 

Log  C. 
FIG.  11.    Comparison  of  Experimental  Values  with  Equation  11  for  KNH2  in  NH3. 

mass^action  law  as  a  limiting  form,  it  follows  that  the  equation  will  be 
applicable  to  the  more  dilute  solutions  in  any  case.  It  remains,  there- 
fore, to  determine  whether  the  equation  likewise  applies  to  the  more 
concentrated  solutions. 

Kraus  and  Bray,6  who  have  examined  the  applicability  of  this  equa- 
tion to  a  large  number  of  non-aqueous  solutions,  including  solutions  in 
ammonia,  have  concluded  that  the  experimental  values  may  be  repre- 


•  Kraus  and  Bray,  lac.  cit. 


FORM  OF  THE  CONDUCTANCE  FUNCTION  73 

sented  by  an  equation  of  this  type  within  the  limits  of  experimental 
error.  In  general,  it  has  been  found  that  the  more  consistent  the  ex- 
perimental data  are  among  themselves,  the  more  nearly  do  they  adjust 
themselves  to  Equation  11.  The  results  for  inorganic  electrolytes  dis- 
solved in  ammonia  are  summarized  in  Table  XXVII. 

TABLE  XXVII. 

CONSTANTS  OP  THE  CONDUCTANCE  FUNCTION  FOR  INORGANIC 
ELECTROLYTES  IN  NH3  AT  — 33°. 

Electrolyte  lO4^  m  D 

KNH2    1.20  1.18  0.095 

Agl   2.90  0.70  0.009 

NH4C1    12.0  0.84  0.127 

KN03  15.5  0.96  0.25 

NaN03  23.0  0.89  0.32 

NH4Br 23.0  0.82  0.24 

LiN03    26.0  0.86  0.34 

Nal    28.0  0.83  0.43 

AgN03    28.0  0.83  0.36 

NH4N03   28.0  0.86  0.39 

KI 42.0  0.94  0.62 

The  values  of  A0  are  not  given  in  this  table,  but  they  will  be  found  in 
Table  XXII.  By  means  of  the  constants  in  these  tables  the  equivalent 
conductances  of  the  various  electrolytes  may  be  calculated  at  any  de- 
sired concentration  within  the  limits  of  experimental  error  up  to  approxi- 
mately normal  concentrations.  It  is  obvious  that  a  comparison  of  the 
ionization  of  different  electrolytic  solutions  may  be  made  by  means  of 
the  constants  given  above.  The  relative  ionization  of  two  salts  will  vary 
as  a  function  of  the  concentration,  since  the  constants  for  the  two  elec- 
trolytes will  not,  as  a  rule,  have  the  same  value.  The  values  of  the 
constant  K  have  already  been  considered  and  need  not  be  further  dis- 
cussed here.  The  values  of  the  constant  D  are  seen  to  lie  within  fairly 
narrow  limits.  Excepting  the  constants  for  potassium  amides  and  silver 
iodide,  the  values  of  D  lie  between  0.127  and  0.62.  and  most  of  the 
values  lie  between  0.24  and  0.43.  There  is  no  fixed  relation  between  the 
values  of  D  and  of  K,  although  in  general  an  electrolyte  with  a  large 
value  of  K  has  a  large  value  of  D.  Thus,  potassium  amide,  silver  iodide 
and  ammonium  chloride  have  the  smallest  values  of  K  and  likewise  they 
have  the  smallest  values  of  the  constant  D.  So,  also,  potassium  iodide, 
which  has  the  highest  value  of  the  constant  K,  likewise  has  the  highest 
value  of  the  constant  D.  Apparently,  the  constants  K  and  D  are  not 


74         PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

entirely  independent  of  each  other,  or,  in  other  words,  they  depend  in 
a  corresponding  manner  upon  some  property  of  the  electrolyte.  The 
values  of  ra  lie  between  0.70  and  1.18  and,  for  the  most  part,  they  lie 
between  0.82  and  0.96.  The  general  form  of  the  curve,  as  we  shall 
presently  see,  is  determined  largely  by  the  value  of  the  constant  ra.  It 
follows,  consequently,  that  the  curves  for  the  various  electrolytes  will  in 
general  be  similar.  No  definite  relation  appears  to  exist  between  the 
values  of  the  constant  ra  and  the  constants  D  and  K.  In  many  cases, 
however,  as  we  shall  see  later,  electrolytes  having  a  small  value  of  K 
and  D  have  a  relatively  large  value  of  ra.  Silver  iodide  is  an  exception 
to  this  rule. 

The  constants  for  a  number  of  organic  electrolytes  are  given  in 
Table  XXVIII. 

TABLE  XXVIII. 

CONSTANTS  OF  EQUATION  11  FOR  ORGANIC  ELECTROLYTES 
IN  NH3  AT  —33°. 

Solute  Ao        104#  ra  D 

Cyanacetamide    260  0.045  1.24  0.026 

Benzenesulphonamide    208  1.39  1.00  0.029 

Methylnitramine    256  8.4  0.85  0.080 

Metanitrobenzenesulphonamide 231  12.5  0.76  0.103 

Nitrourethaneammonium 262  21.6  0.76  0.22 

Trinitraniline 234  30.0  0.73  0.38 

They  have  been  arranged  in  the  order  of  increasing  values  of  K.  It  is 
at  once  evident  that  there  is  no  relation  between  the  various  constants 
and  the  value  of  A0.  On  the  other  hand,  there  is  apparently  a  rough 
parallelism  between  the  constants  K  and  D.  The  order  of  the  K  and  D 
constants,  in  other  words,  is  identical.  The  order  of  the  constant  ra 
appears  to  be  the  reverse  of  that  of  the  constants  D  and  K;  that  is,  as 
K  and  D  increase,  ra  decreases. 

Aside  from  solutions  in  liquid  ammonia,  the  equation  has  been  found 
to  hold  for  solutions  in  sulphur  dioxide,7  amyl  and  propyl 8  alcohols  and 
phenol.9  In  the  case  of  the  sulphur  dioxide  solutions  the  equation  holds 
within  the  limits  of  experimental  error.  In  that  of  the  alcohol  solu- 
tions, the  deviations  appear  to  be  considerable  at  certain  points,  but  it  is 
possible  that  these  are  due  either  to  experimental  errors  or  to  a  lack  of 
proper  adjustment  of  the  constants.  The  constants  found  are  as  follows: 

7  Kraus  and  Bray,  loc.  cit. 

•Keyes  and  Winninghoff,  J.  Am.  Chem.  Soc.  38,  1178   (1916). 

•Kurtz,  Thesis,  Clark  University  (1921). 


FORM  OF  THE  CONDUCTANCE  FUNCTION  75 

TABLE   XXIX. 
CONSTANTS  OF  EQUATION  11  FOR  SOLUTIONS  IN  DIFFERENT  SOLVENTS. 

Solvent  Solute  m  K                 D  AO 

Sulphur  dioxide  .....  KI  1.14  8.5  X  10'4  0.403  207. 

Iso-amyl  alcohol  ____  Nal  1.2  5.85  X  1Q-4  0.374  7.79 

Propyl  alcohol   .....  Nal  0.75  38.3  X  10~4  0.208  20.1 

Phenol  .............  (CH3)4NI  1.28  2.3  X  10~4  0.69  16.67 

Comparing  the  ionization  in  ammonia  and  sulphur  dioxide,  in  view 
of  the  much  lower  value  of  the  constant  K,  dilute  solutions  in  sulphur 
dioxide  are  ionized  to  a  much  smaller  extent  than  are  solutions  in  am- 
monia. On  the  other  hand,  in  the  more  concentrated  solutions,  the  ioniza- 
tion values  again  approach  each  other,  since  the  value  of  D  for  sulphur 
dioxide  is  relatively  large  and  the  value  of  m  is  much  greater  than  that 
in  ammonia.  The  conductance  curves  of  solutions  in  sulphur  dioxide, 
phenol  and  amyl  alcohol  pass  through  a  minimum  while  that  of  solu- 
tions in  propyl  alcohol  resembles  the  curve  for  aqueous  solutions. 

In  the  case  of  a  great  many  solutions  whose  ionization  is  relatively 
low,  the  limiting  value  of  the  equivalent  conductance  in  dilute  solutions 
cannot  be  determined.  Under  these  conditions,  the  value  of  K  remains 
indeterminate.  Nevertheless,  if  the  ionization  is  relatively  low,  the  ap- 
plicability of  Equation  11  may  be  tested  approximately.  It  is  apparent 
that,  when  the  ionization  is  low,  the  constant  K  becomes  negligible  in 
comparison  with  the  term  involving  the  constant  D.  Also,  the  value 
of  A  becomes  small  in  comparison  with  that  of  A0,  so  that  for  purposes 
of  approximation  the  value  of  A  may  be  neglected  in  comparison  with 
that  of  A0.  Under  these  conditions  Equation  11  reduces  to  the  form: 

(12)  CA2  =  D  A02  —  m  (CA)  ™  9 
For  the  sake  of  brevity  we  may  write: 

(13)  DA02  —  m=P. 


If  we  take  the  logarithm  of  both  sides  of  this  equation,  we  obtain  the 

linear  equation: 

(14)  log  CA2  =  m  log  CA  +  log  P. 

In  order  to  test  the  applicability  of  the  equation  to  solutions  of  very  low 
ionization,  therefore,  it  is  only  necessary  to  plot  the  logarithms  of  the 
values  of  CA  and  of  CA2,  both  of  which  may  be  obtained  from  experi- 
mental data.  If  the  equation  holds,  the  points  will  lie  upon  a  straight 


76 


PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 


line,  the  slope  of  which  gives  the  value  of  the  constant  m  and  the  inter- 
cept on  the  axis  of  CA2  the  value  of  P. 

In  Figure  12  are  shown  plots  of  Equation  14  for  a  number  of  organic 
electrolytes  dissolved  in  hydrobromic   and  in  hydriodic   acids  and  in 


3-0  3-5 


2.5  i.o 

Log(cA) 


FIG.  12.    Illustrating  the  Applicability  of  Equation  11  to  Solutions  of  Binary  Elec- 
trolytes in  Solvents  of  Low  Dielectric  Constant. 

hydrogen  sulfide.  These  solutions  are  well  adapted  to  the  purpose  of 
testing  the  applicability  of  the  equation,  since  the  ionization  of  electro- 
lytes in  these  solvents  is  extremely  low.  It  is  evident  that,  except  in  the 
case  of  a  few  very  concentrated  solutions,  the  equation  holds  within  the 
limits  of  experimental  error.  The  curves,  in  general,  have  approximately 


FORM  OF  THE  CONDUCTANCE  FUNCTION          77 

the  same  slope,  which  follows  from  the  fact  that  the  value  of  m  is  ap- 
proximately the  same  for  these  solutions.  The  greater  the  value  of  the 
exponent  m,  the  steeper  the  curve  on  the  plot.  A  great  many  solutions 
of  this  type  have  been  measured  and  the  results  have  been  compared 
with  the  equation.  The  deviation  in  no  case  appears  to  be  very  great, 
from  which  it  may  be  concluded  that  the  equation  holds  to  a  considerable 
degree  of  approximation.  The  values  of  the  constants  m  and  P  for 
various  solutions  are  given  in  Table  XXX.10 

Many  of  the  substances  which  appear  in  this  table  are  not  ordinarily 
classed  as  typical  electrolytes.    They  are,  in  general,  basic  compounds 

TABLE  XXX. 

VALUES  OF  THE  CONSTANTS  OF  EQUATION  12  FOR  VARIOUS  SOLUTIONS. 
Liquid  Hydrochloric  Acid  (HC1). 

Tempera- 
Solute  Formula  ture  m  P 

Triethylammonium  chloride  (C2H5)3N.HC1        —100°  1.42  5.75 

Acetamide  CH3CONH2  —100°  1.40  5.53 

Methylcyanide    CH3CN  —100°  1.44  4.17 

Resorcinol  C6H4(OH)2  —89°  1.18  3.89 

Hydrocyanic   acid    HCN  —100°  1.46  3.33 

Toluic  acid CH3 .  C6H4COOH       —  96°  1.52  1.58 

Diethylether  (C2H5)2O  —100°  1.51  1.38 

Propionic  acid C2H5COOH  —  96°  1.47  1.21 

Acetic  acid  CH.COOH  —96°  1.42  1.09 

Benzoic  acid C6H5COOH  —  96°  1.42  0.94 

Butyric  acid C3H7COOH  —  96°  1.45  0.85 

Methylalcohol  CH3OH  —89°  1.61  0.71 

Formic  acid HCOOH  —  96°  1.55  0.67 

Ethylalcohol    C2H5OH  —89°  1.70  0.50 

Butylalcohol    C4H9OH  —89°  1.62  0.38 

Liquid  Hydrobromic  Acid  (HBr). 

Triethylammonium    chloride  (C2H5)3N.HC1  —81°  1.51  4.03 

Thymol    CH3 .  C3H7 .  C6H3OH  —  80°  1.57  3.60 

Methylcyanide    •. . .  CH3CN  —81°  1.53  2.48 

Acetamide    CH3CONH2  —81°  1.48  2.29 

Acetone   (CH3)2CO  —81°  1.63  1.88 

Metacresol  m-CH3.C6H4OH  —80°  1.54  1.70 

Orthonitrotoluene  o-CH3 .  C6H4NO2  —81°  1.50  0.99 

Benzoic  acid  C6H5COOH  —  80°  1.67  0.82 

Acetic  acid  CH3COOH  —  80°  1.66  0.78 

10  Kraus  and  Bray,  loc.  cit. 


78          PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

TABLE   XXX.—  Continued. 
Liquid  Hydrobromic  Acid  (HBr). 

Tempera- 

Solute                                     Formula                 ture  m  P 

Metatoluic  acid  ...........     m-CH3  .  C6H4COOH  —  80°  1  .65  0.77 

Paratoluic  acid  ...........     p-CH3  .  C6H4COOH   —  80°  1.62  0.76 

Butyric  acid   .............     C3H7COOH                —80°  1.66  0.71 

Orthotoluic  acid  ..........     o-CH3C6H4COOH     —  80°  1.60  0.65 

Diethylether  ..............      (C2H5)20                    —81°  1.63  0.59 

Paracresol    ...............     p-CH3.C6H4OH         —80°  1.66  0.55 

Resorcinol    ...............     C6H4(OH)2                 —80°  1.40  0.52 

Orthocresol   ...............     o-CH3.C6H4OH         —80°  1.68  0.45 

Methylalcohol  ............     CH3OH                       —80°  1.80  0.41 

Allylalcohol    ..............     C2H3.CH2OH            —80°  1.79  0.39 

Ethylalcohol  ..............     C2H5OH                     —80°  1.80  0.35 

Amylalcohol   ..............     C^OK                    —80°  1.84  0.27 

Normal  propylalcohol  .....     n-C3H7OH                  —80°  1.77  0.27 

Phenol   ...................     C6H5OH                     —80°  1.61  0.27 

Liquid  Hydriodic  Acid  (HI). 

Triethylammonium    chloride     (C2H5)3N.HC1          —50°  1.58  2.69 

Ethylbenzoate  ............     CC)H5COOC2H5           —50°  1.62  2.09 

Diethylether  ........  ......      (C2H5)20                    —50°  1.66  1.26 

Liquid  Hydrogen  Sulfide   (H2S). 

Triethylammonium    chloride     (C2H5)3N.HC1          —81°  1.58  2.06 

Nicotine   .................     C10H14N2                    —81°  1.63  1.20 

Mercuric  Chloride  (HgCl2). 

Caesium  chloride  .........     CsCl                               282°  1.20  14.5 

Potassium  chloride  ........     KC1                                282°  1.21  14.3 

Ammonium  chloride  .......     NH4C1                           282°  1.22  14.3 

Sodium  chloride  ...........     NaCl                             282°  1.29  13.7 

Cuprous  chloride  ..........     CuCl                             282°  1.33  13.6 

Liquid  Iodine  (I2). 

Potassium  iodide  .......  ...     KI                                 140°  1.44  13.5 

Ethylamine  (C2H5NH2'). 

Silver  nitrate  .............     AgN03                              0°  1.42  4.68 

Ammonium  chloride  .......     NH4C1                               0°  1.57  1.97 

Lithium  chloride  ..........     LiCl                                   0°  1.54  1.80 


Amylamine  (Cg 
Silver  nitrate  .  ............     AgN03  25°      1.67      1.97 


FORM  OF  THE  CONDUCTANCE  FUNCTION  79 

TABLE  XXX.— Continued. 
Aniline  (C6H5NH2). 

Tempera- 
Solute  Formula  ture          m          P 

Ammonium  iodide NH4I  25°  1.44  2.19 

Silver  nitrate  AgN03  25°  1.42  2.02 

Pyridine  hydrobromide  . . . .  C5H5N.HBr  25°  1.51  1.91 

Aniline  hydrobromide C6H5NH2.HBr  25°  1.44  1.29 

Lithium  iodide Lil  25°  1.33  1.04 

Methyl  Aniline  (C6H5NHCH3). 

Pyridine  hydrobromide C5H5N.HBr  25°       1.64      1.19 

Aniline  hydrobromide C6H5NH2.HBr  25°       1.59      0.59 

Acetic  Acid  (CH3COOH). 

Lithium  bromide    LiBr  25°  1.43  2.60 

Pyridine C5H5N  25°  1.56  1.86 

Dimethylaniline    C6H5N(CH3)2  25°  1.48  1.53 

Aniline    C6H5NH2  25°  1.52  1.32 

Propionic  Acid  (C2H5COOH). 

Lithium  bromide LiBr  25°       1.74      0.84 

Aniline   C6H5NH2  25°      1.79      0.37 

Pyridine  C5H5N  25°       1.76      0.32 

Bromine  (Br2). 

Trimethylammoniumchlo- 

ride11  (CH3)3NHC1  18°      1.62      0.55 

Iodine12   I2  25°      1.74      0.17 

containing  either  oxygen  or  nitrogen  and  in  all  likelihood  they  owe  their 
electrolytic  properties  to  the  formation  of  complexes  with  the  solvent, 
in  which  oxygen  and  nitrogen  exhibit  basic  properties.  For  a  given 
value  of  m  the  ionization  is  in  general  the  greater  the  greater  the  value 
of  P.  It  is  apparent  that  among  these  electrolytes  the  typical  salts  are 
the  most  highly  ionized.  In  solutions  in  the  halogen  acids  and  hydrogen 
sulphide,  the  substituted  ammonium  salts,  or  their  derivatives,  are  more 
highly  ionized  than  are  other  substances.  In  general,  also,  the  typical 
salts  have  values  of  the  constant  m  smaller  than  those  of  electrolytes 
which  have  a  lower  ionization.  There  are,  however,  a  few  exceptions, 
such,  for  example,  as  resorcinol  in  hydrochloric  acid,  which  has  a  value 

"Darby,  J.  Am.  Chem.  Soc.  40,  347  (1918). 

"Plotnikow  ana  Rokotjan,  Ztschr.  f.  phya.  Chem.  84,  365   (1913). 


80          PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

of  m  of  only  1.18.  Correspondingly,  resorcinol  in  hydrobromic  acid  has 
a  constant  of  only  1.40,  which  is  distinctly  lower  than  that  of  other  sub- 
stances dissolved  in  this  solvent.  It  is  interesting  to  note  that  the  value 
of  the  constant  m  never  exceeds  2.  The  highest  value  of  this  constant  is 
1.80  for  methyl  and  ethyl  alcohols  in  hydrobromic  acid.  It  appears  prob- 
able that  the  values  of  m  for  these  two  substances  in  hydrogen  iodide 
will  be  found  greater  than  in  hydrogen  bromide. 

In  fused  mercuric  chloride  the  different  typical  salts  exhibit  a  very 
similar  behavior.  The  constant  P  differs  only  inappreciably  for  different 
electrolytes  and  the  values  of  the  constant  m,  for  the  most  part,  fall 
within  very  narrow  limits. 

In  the  amines  the  constant  m  increases  and  the  constant  P  decreases 
as  the  organic  radical  becomes  more  complex.  The  same  is  true  in  the 
case  of  acetic  and  propionic  acids,  where  the  constant  m  for  propionic 
acid  is  much  greater  than  for  acetic  acid.  Judging  by  the  relatively  low 
value  of  the  constant  m  for  liquid  iodine,  this  substance  is  a  fairly  good 
ionizing  agent. 

2.  Geometrical  Interpretation  of  the  Conductance  Function.  The 
conductance  function: 


—  Y 

may  be  interpreted  most  readily  by  graphical  methods.    It  will  be  under- 

stood that  y  =  T—  and  that  the  following  equations  may  at  once  be  con- 
A0 

verted  to  equations  in  which  CA  and  A  appear  as  variables  in  place  of 
CY  and  Y-  In  speaking  of  the  ionization,  it  is  not  intended  to  convey  the 
impression  that  the  conductance  ratio  necessarily  measures  the  ioniza- 
tion, but  rather  it  is  introduced  as  a  convenient  variable  for  the  purpose 
of  discussion.  If  we  differentiate  the  above  equation,  we  have: 


(15)  ____       , 

''    d(Cy) 


dv 

The  coefficient  ,     *  .,  which  is  the  tangent  to  the  Y>    CY-curve,  is  a 

measure  of  the  change  of  the  ionization  as  a  function  of  the  ion  concen- 
tration at  any  point  on  the  curve.     It  is  evident  that  if  the  term 

~  ..„  .    approaches  zero  as  CY  approaches  zero,  the  tangent  will  ap- 
proach the  value  —  ^  as  a  limit,  where  K  is  the  limit  which  K'  ap- 


FORM  OF  THE  CONDUCTANCE  FUNCTION  81 

preaches  at  zero  concentration.     At  higher  concentrations  the  tangent 
will  decrease;  that  is,  the  ionization  will  increase  less  rapidly  for  a  given 

increase  in  the  ion  concentration,  because  both  K'  and  -^  ,.~  >   in- 

crease with  the  concentration. 

If  we  introduce  A  and  CA  as  variables,  Equation  15  has  the  form: 

dA  A*     /CA      dJC' 


-2''    d(CA)       • 


The  plot  of  A  against  the  specific  conductance  in  dilute  solution  will 
therefore  be  a  curve  convex  toward  the  axis  of  specific  conductances,  and 
as  the  concentration  decreases  it  will  approach  a  line  whose  tangent  is 

—       provided  the  conditions  mentioned  in  the  preceding  paragraph  are 
K. 

fulfilled. 

In  order  to  follow  up  the  form  of  the  curve  at  higher  concentrations, 
we  may  introduce  the  conductance  function  11.  On  differentiating  this 
function  we  have: 

(17)  "  A2 

Since  K'  approaches  K  at  low  concentrations,  it  follows  that  the  tangent 
approaches  the  value  —  -=•  as  a  limit.  At  higher  concentrations,  the 

tangent  decreases,  since  K'  decreases.  Ultimately  the  form  of  the  curve 
depends  upon  the  value  of  m.  If  m  is  less  than  1,  then  the  tangent  will 
always  have  a  negative  value;  in  other  words,  the  equivalent  conduct- 
ance will  always  decrease  with  increasing  values  of  the  specific  con- 
ductance. On  the  other  hand,  when  m  is  greater  than  unity,  the  tangent 
will  become  zero,  when: 

(18) 

J.\. 

that  is,  at  this  point  the  conductance  passes  through  a  minimum  value 
after  which  it  increases  with  increasing  values  of  the  specific  conduct- 

(CA\m 
-r—  1    +  K,  and  denoting  by  C' 

and  A'  the  values  of  the  concentration  and  the  equivalent  conductance  at 
the  minimum  point,  we  have: 

(19) 


D(m-D) 


82          PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 
where  y'  ='r~'    This  e(lua^on  gives  the  value  of  the  specific  conductance, 

A0 

or  the  ion  concentration,  at  the  minimum  point.    The  value  of  the  ioniza- 
tion  follows  from  the  equation: 

Y'       _ 


When  m  equals  1,  we  have  a  limiting  case  in  which  Equation  18  reduces 
to: 

dA  A2       mK 


(21) 


Kft 


rr 

It  is  evident  that  since  -^  decreases  as  the  concentration  increases,  the 

tangent  approaches  a  value  zero  at  high  concentration.  The  ionization, 
therefore,  approaches  a  constant  value  which  may  be  obtained  by  writing 
m  =  1  in  Equation  11;  we  have: 


or,  neglecting  K, 

(22)  ^  „  =  D      or      Yf  =  YT^- 

The  ionization  of  such  solutions,  therefore,  approaches  the  value  -z — . 


as  a  limit.  If  an  electrolyte  has  a  very  small  value  of  K  and  a  relatively 
large  value  of  D,  while  the  value  of  m  is  nearly  unity,  the  conductance 
will  vary  only  very  little  with  concentration  at  higher  concentrations. 
This  is  the  case  with  the  cyanides  in  liquid  ammonia,  more  particularly 
with  the  cyanides  of  gold  and  silver.  The  value  of  m  is  a  little  less  than 
unity  for  the  first  substance  and  a  little  greater  than  unity  for  the 
second.13  For  the  ion  concentration  Cy  —  1,  Equation  11  reduces  to: 


and  since  K  may  be  neglected  at  this  concentration,  we  have: 
(23) 

The  constant  D,  therefore,  measures  the  ratio  of  the  ionized  to  the  un- 
ionized fraction  at  the  concentration  CY  =  1.    We  shall  see  that,  for  a 

"  Kraus  and  Bray,  loc.  cit.,  p.  1360. 


FORM  OF  THE  CONDUCTANCE  FUNCTION  83 

given  substance  in  different  solvents  or  in  the  same  solvent  at  different 
temperatures,  the  value  of  D  is  practically  constant,  while  the  values  of 
m  and  K  vary.  It  follows,  therefore,  that  the  y,  Cy-curves  for  all  such 

solutions  pass  through  the  point  Cy  =  1,  Y  =  n  _i_  i  •    ^is  relation  is  of 

importance  in  interpreting  the  influence  of  temperature  on  the  conduct- 
ance of  solutions. 

The  further  discussion  of  the  relation  between  the  conductance  and 
the  concentration  is  greatly  simplified  by  introducing  the  function  K'  and 
examining  the  manner  in  which  K'  varies  as  a  function  of  the  ion  concen- 
tration. Differentiating,  we  have  the  equations: 


A0W 
(24) 

^-JMPtJP* 

If  D  were  zero,  that  is,  if  the  mass-action  law  held,  we  should  have: 


. 

or  K'  =  constant. 

On  the  other  hand,  when  the  D  term  is  present,  K'  will  always  increase 
with  the  concentration.  The  form  of  the  K',  CA-curve  is  determined 
mainly  by  the  constant  m.  When  m  =  1,  we  evidently  have: 


(26)  =  Dm      or 


In  this  limiting  case,  therefore,  K'  varies  as  a  linear  function  of  the 
specific  conductance  CA. 

The  form  of  the  curves  for  values  of  m  greater  and  less  than  unity 
may  readily  be  determined  by  means  of  the  second  differential  coefficients. 
W^e  have: 

(27)  3^T5=D«(»-1) 

When  m  <  0, 

(28) 


and  the  K,  Cy-curve  is  everywhere  concave  toward  the  axis  of  Cy.    When 


84          PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 


and  the  curve  is  everywhere  convex  toward  the  Cy-axis.    In  the  limiting 
case,  m  =  1,  and 

(30) 


and  K  is  a  linear  function  of  Cy. 

From  Equation  24,  it  follows  that  when  m  <  1, 

dK' 

<31>  c!Lmo  d(CA)=  °° 

and  when  m  >  1, 


In  the  first  case  the  K',  Cy-curve  approaches  the  limit  K  asymptotic 
to  the  axis  of  K',  while  in  the  second  case  it  approaches  the  limit 
asymptotic  to  a  line  parallel  to  the  axis  of  Cy. 

The  curvature  of  both  curves  increases  as  the  concentration  de- 
creases.1* For  the  radius  of  curvature  of  the  K',  Cy-curve  we  have  the 
equation: 

2(2-w») 

,    mV*JH/3    (CY) 
" 


[Dm(m  —  I)]3/2  (m  —  I)2/3 

The  exponent  2—  m  of  the  first  term  of  the  right-hand  member  of  this 
equation  is  positive  for  all  values  of  m  less  than  2.  Since  no  solutions 
are  known  for  which  m  is  greater  than  2,  we  need  not  consider  greater 
values  of  m.  It  is  evident,  therefore,  that,  due  to  the  first  term,  the 
radius  of  curvature  increases  with  Cy  for  all  values  of  m.  For  m  >  1,  the 
coefficient  2m  —  1  is  positive  and  the  radius  of  curvature  increases  with 
Cy  due  to  this  term  also.  When  m  <  1,  2  —  m  >  2m  —  1  so  long  as  m  is 
greater  than  zero.  It  follows,  therefore,  that  the  first  term  overbalances 
the  second  and  that  the  curvature,  for  all  values  of  m  between  zero  and  2, 
decreases  with  increasing  concentration,  becoming  infinite  in  the  limit. 
For  m  =  1,  R  =  oo,  and  the  curvature  is  zero.  For  m  <  1,  the  curvature 
is  negative;  that  is,  the  curve  is  concave  toward  the  Cy-axis.  While  for 
m  >  1,  the  curvature  is  positive,  and  the  curve  is  convex  toward  this  axis. 
For  given  values  of  D  and  K  and  for  different  values  of  m  we  have  a 
family  of  curves  passing  through  the  points  Cy  =  0,  K'  =  K  and  Cy  =  1, 
K'  —  D  -}-  K.  Such  a  system  of  curves  is  shown  in  Figure  13.  The  con- 

14Kraus,  J.  Am.  Chem.  Soc.  £2,  6  (1920). 


FORM  OF  THE  CONDUCTANCE  FUNCTION 


85 


stants  assumed  are:  D  =  1.703,  K  =  0.001,  and  A0  =  129.9  for  all  curves, 
while  ra  =  0.52  for  Curve  I,m  =  1.50  for  Curve  II,  and  ra  =  1  f or  Curve 
III.  The  greater  the  value  of  ra,  the  less  rapidly  does  K'  increase  at  the 
lower  concentrations.  For  a  value  of  m  =  0,  the  curve  degenerates  into 
a  horizontal  straight  line,  corresponding  to  the  mass-action  constant 
K'  =  K  +  D. 


.8 


1.6 


1.4 


1.2 


0.4 


0.1 


CUPVlfy 


/fa*t 


0.1 


0.2       0.3      0.4      0.5       0.6 

Ion  Concentration  (Cy). 


0.7      0.8       09 


FIG.  13.    Showing  Typical  K'  Curves  for  Different  Values  of  m  According  to 

Equation  11. 

It  is  evident  that  a  given  percentage  deviation  of  K'  with  respect  to 
K  will  be  found  at  different  values  of  the  ion  concentration.  If  we  con- 
sider two  solutions  for  which  the  value  of  K'  has  increased  by  a  given 
percentage  amount  over  K  in  both  cases,  then  the  ion  concentrations  of 
the  two  solutions  are  related  according  to  the  equation: 


(34) 


K 


If  D/K  for  the  two  solutions  is  of  the  same  order,  then  the  ratio  of 
the  ion  concentrations  will  depend  upon  the  values  of  ra.  The  smaller 
the  value  of  ra,  the  lower  will  be  the  ion  concentration  at  which  a  given 
change  in  K  will  be  found.  This  is  also  obvious  from  Figure  13.  For 


86          PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

a  given  rise  in  the  curve  above  the  value  of  K,  the  ion  concentration  will 
be  the  smaller,  the  smaller  the  value  of  ra.  The  value  of  the  ion  concen- 
trations corresponding  to  any  given  value  of  Kf  are  found  by  drawing  a 
horizontal  line  and  reading  off  the  concentrations  at  the  points  of  inter- 
section. In  Table  XXXI  are  given  the  values  of  ra,  D/K,  and  the  ion 

TABLE   XXXI. 

VALUE  OF  D/K  AND  OF  ra  AND  CONCENTRATIONS  AT  WHICH  GIVEN  DEVIA- 
TIONS FROM  THE  MASS-  ACTION  LAW  OCCUR  FOR  SOLUTIONS  IN  NH3. 

; 

Electrolyte  D/K  X  10-2        m      K'~  K  ~ 


A  A 

CX10*  CyXlQ4  CX104 

KNH2    .............  ........  7.91  1.18  2.76  8.82  8.97  65.0 

Agl   ........................  0.345  0.70  0.86  1.14  6.38  18.03 

NH4C1  ............  .  ......  .  .  1.06  0.84  1.10  1.19  5.70  7.99 

KN03   ......................  1.35  0.89  1.35  1.46  6.89  10.80 

NaN03    ....................  1.39  0.89  1.33  1.42  6.52  8.06 

NH4Br   ..............  :  ......  1.04  0.82  0.89  0.92  4.85  5.70 

LiN03    .....................  1.31  0.86  1.06  1.10  5.33  6.32 

Nal    .......................  1.54  0.83  0.63  0.64  3.33  3.66 

AgN03    .....................  1.29  0.83  0.78  0.80  3.38  3.80 

NH4N08   ....................  1.39  0.86  0.98  1.02  4.92  5.64 

KI    ........................  1.43  0.94  2.03  2.12  8.91  10.50 

Cyanacetamide  ..............  55.8  1.24  0.83  15.4  2.53  120.0 

Benzenesulphonamide    ........  2.09  1.00  2.40  6.34  9.59  64.8 

Methylnitramine  ............  0.941  0.85  1.32  1.52  7.08  12.04 

Metanitrobenzenesulphonamide  0.825  0.76  0.58  0.61  3.62  4.49 

Nitrourethaneammonium    .....  1.02  0.76  0.44  0.45  2.74  3.03 

Trinitraniline  ...............  1.27  0.73  0.22  0.22  1.45  1.49 

concentrations  Cy  and  the  total  salt  concentrations  at  which  the  increase 
over  the  values  of  K  amounts  to  5  and  20  per  cent  respectively. 

For  approximately  the  same  value  of  D/K  the  value  of  Cy,  for  which 
a  given  increase  occurs  in  the  value  of  the  mass-action  function,  decreases 
as  m  decreases.  Thus,  in  the  case  of  benzenesulphonamide,  methyl- 
nitramine,  metanitrobenzenesulphonamide,  and  trinitraniline,  the  value  of 
m  decreases  from  1.0  to  0.73,  while  the  value  of  Cy  for  a  5%  increase  in 
the  function  decreases  from  2.40  to  0.22.  Similarly,  in  the  case  of  sodium 
and  potassium  iodides,  the  values  of  ra  are  respectively  0.83  and  0.94, 
and  the  values  of  the  ion  concentrations  for  a  5%  increase  in  the  func- 
tion are  0.63  and  2.03  respectively.  The  deviations  from  the  simple 
mass-action  law,  at  a  given  concentration  therefore  appear  smaller  in  the 
case  of  potassium  iodide  than  in  that  of  sodium  iodide.  For  the  same 


FORM  OF  THE  CONDUCTANCE  FUNCTION  87 

value  of  the  constant  m,  a  given  deviation  occurs  at  the  lower  concen- 
tration, the  greater  the  value  of  D/K.  Thus,  sodium  iodide  and  silver 
nitrate  both  have  a  value  of  the  exponent  m  =  0.83,  while  the  values  of 
D/K  are  1.54  and  1.29  respectively.  Correspondingly,  the  values  of  the 
ion  concentrations  for  a  5%  increase  of  the  function  are  0.63  and  0.78 
respectively.  The  value  of  D/K  for  typical  electrolytes  in  ammonia  lies 
in  the  neighborhood  of  iOO.  For  weak  electrolytes  the  value  of  D/K 
appears  to  be  larger,  as  for  example  for  cyanacetamide  and  potassium 
amide.  In  the  case  of  silver  iodide,  however,  which  appears  to  be  a  very 
exceptional  electrolyte,  the  value  of  D/K  is  extremely  small.  As  we  shall 
see  below,  the  value  of  D  for  a  given  electrolyte  is  relatively  independent 
of  the  nature  and  condition  of  the  solvent.  At  higher  temperatures,  the 
dielectric  constant  of  the  solvent  decreases  and  with  it  there  is  a  large 
decrease  in  the  value  of  the  constant  K,  while  the  constant  D  remains 
practically  fixed.  At  higher  temperatures,  therefore,  the  value  of  D/K 
will  increase.  This  tends  to  increase  the  deviations  from  the  simple 
mass-action  relation.  On  the  other  hand,  the  value  of  m  increases  with 
increasing  temperature  and  decreasing  dielectric  constant,  and  this  tends 
to  make  the  percentage  deviations  from  the  simple  mass-action  relation 
smaller.  The  observed  effect  will  be  the  resultant  of  these  two.  From 
the  known  form  of  the  conductance  curve  in  solvents  of  very  low  dielec- 
tric constant,  it  is  evident  that  ultimately  the  effect  due  to  the  increase 
in  the  value  of  D/K  overbalances  that  due  to  the  increase  in  the 
value  of  m. 

Corresponding  to  the  K'  ',  Cy-curves,  we  have  the  y,  Cy-curves.    These 
curves    pass    through    the    common    points    y  =  1>  <?Y  =  0,   and    y  = 


The  particular  case  when  the  value  of  m  is  equal  to  unity,  which 
leads  to  a  linear  relation  between  the  function  K'  and  the  ion  concentra- 
tion, likewise  yields  a  very  simple  relation  between  the  equivalent  con- 
ductance and  the  specific  conductance.  In  this  case  we  may  write  our 
equation  : 


(35)  or 

^o- 

It  is  obvious  that  the  ratio  ^—  — ^-,  or  what  is  proportional  to  it,  the  ratio 

Y 
j— — ,  is  now  a  linear  function  of  the  reciprocal  of  the  specific  conduct- 


88      PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

ance  or  of  the  ion  concentration.    The  equation  obviously  approaches  in 
form  that  which  follows  from  the  mass-action  law  which  is: 

'  K 


If  the  mass-action  law  holds,  the  ratio  of  the  ionized  to  the  un-ionized 
fraction  is  inversely  proportional  to  the  ion  concentration.  If,  therefore, 

v 
we  were  to  plot  the  values  of  the  ratio  •=  —  -  —  against  values  of  the  ion 

concentration  Cy,  we  should  obtain  a  rectangular  hyperbola.  When  the 
constant  ra  equals  unity,  the  equation  is  of  the  same  form,  except  that 
the  entire  curve  is  raised  by  an  amount  equal  to  D.  In  this  case,  there- 

Y 


fore,  the  curve  is  again  a  rectangular  hyperbola  asymptotic  to  the 


1-Y 


axis  on  one  side  and  asymptotic  to  the  horizontal  line  y— - —  =  D  on  the 

other. 

In  very  concentrated  solutions,  in  the  case  of  substances  for  which  the 
value  of  ra  does  not  differ  too  greatly  from  unity,  the  equivalent  con- 
ductance at  a  given  concentration  for  different  electrolytes  is  roughly 
proportional  to  the  value  of  D.  The  value  of  this  constant,  as  has  already 
been  pointed  out,  is  in  a  large  measure  a  distinctive  property  of  the 
electrolyte  and  varies  only  little  as  a  function  of  the  solvent.  For  the 
strongest  electrolytes  the  value  of  D  is  always  of  the  same  order. 

As  we  shall  see  later,  the  conductance  of  an  electrolyte  is  a  function 
of  the  temperature.  At  very  high  and  very  low  concentrations  the  con- 
ductance invariably  increases  with  increasing  temperature,  while,  at  in- 
termediate concentrations,  the  conductance  in  many  cases  decreases  with 
increasing  temperature,  and  always  decreases  at  high  temperatures.  As 
we  shall  see,  this  behavior  is  due  to  the  fact  that  the  value  of  D  remains 
constant  and  independent  of  the  temperature,  while  the  constant  ra 
varies,  increasing  with  increasing  temperature.  At  intermediate  concen- 
trations, therefore,  the  ionization  decreases  with  increasing  temperatures 
whereas  at  very  high  and  very  low  concentrations  the  ionization  remains 
practically  fixed. 

3.  Relation  between  the  Properties  of  Solvents  and  Their  Ionizing 
Power.  Various  attempts  have  been  made  to  connect  the  power  of  a 
solvent  to  ionize  dissolved  substances  with  the  properties  of  this  solvent. 
So,  for  example,  it  has  been  suggested  that  those  solvents  which  are 
normally  associated  are  capable  of  dissociating  substances  dissolved  in 
them.  This  relation,  however,  is  not  a  general  one  for  it  is  now  known 


FORM  OF  THE  CONDUCTANCE  FUNCTION  89 

that  all  liquid  substances  are  capable  of  ionizing  substances  dissolved  in 
them  quite  irrespective  of  what  their  properties  may  be.  The  only  con- 
dition necessary  in  order  that  the  solution  shall  conduct  the  current  is 
that  the  electrolyte  shall  be  sufficiently  soluble  so  that  a  highly  concen- 
trated solution  may  be  obtained.  We  have  seen,  in  the  preceding  section, 
that  in  solvents  which  have  a  low  ionizing  power  the  conductance  de- 
creases with  decreasing  concentration,  and  appears  to  approach  a  value 
of  zero.  If  the  electrolyte,  therefore,  is  not  very  soluble,  its  influence  on 
the  conductance  of  the  solvent  will  be  inappreciable.  If,  however,  an 
electrolyte  is  soluble  up  to  concentrations  as  high  as  normal,  then  its 
solutions  will  in  all  cases  be  found  to  conduct  the  current.  In  general, 
the  typical  inorganic  electrolytes  are  not  soluble  in  weak  ionizing  agents, 
but  certain  organic  electrolytes,  such  as  the  salts  of  organic  bases,  are 
quite  soluble  and  yield  solutions  which  conduct  the  current.  It  is  prob- 
able that  all  liquid  dielectric  media  to  some  extent  possess  the  power  of 
ionizing  substances  dissolved  in  them. 

The  difference  between  the  properties  of  solutions  of  electrolytes  in 
different  solvents  does  not  consist  in  a  power  to  ionize  an  electrolyte  in 
one  case  and  the  entire  absence  of  this  power  in  another,  but  rather  in 
a  difference  in  the  form  of  the  conductance  curve  which  varies  with  the 
nature  of  the  solvent,  either  with  its  constitution  or  with  its  temperature. 
That  property  of  the  solvent  which  appears  to  control  the  form  of  the 
conductance  curve  is  the  dielectric  constant.  Thomson 15  and  Nernst 16 
first  suggested  that  the  ionizing  power  of  a  solvent  is  determined  by  its 
dielectric  constant.  This  constant,  however,  is  by  no  means  to  be  taken 
as  a  measure  of  the  ionizing  power  of  a  solvent,  for  the  ionization  curve 
of  a  given  electrolyte  is  a  complex  function  of  the  concentration  and  the 
relative  ionizations  will  vary  with  the  concentration.  At  very  high  con- 
centrations the  relative  ionizations  will,  in  general,  differ  much  less  than 
at  low  concentrations.  Indeed,  in  the  preceding  section  we  saw  that  the 
constant  D  determines  the  ionization  at  very  high  concentrations  and 
that,  therefore,  for  a  given  electrolyte  in  different  solvents  there  is  a 
certain  concentration  at  which  the  ionization  of  this  electrolyte  will  be 
practically  the  same  in  all  solvents.  What  we  must  expect  to  find,  there- 
fore, is  that  the  form  of  the  conductance  curve  is  determined  by  the 
dielectric  constant  of  the  solvent.  The  relation  between  the  conductance 
and  the  dielectric  constant  is  therefore  shown  most  readily  by  bringing 
out  the  relation  between  the  constants  of  the  conductance  function  and 
the  dielectric  constant.  In  the  following  table  are  given  values  of  the 

"Thomson.  Phil.  Mag.   [5]  36,  320   (1893). 
"Nernst,  Ztschr.  f.  phys.  Chem.  IS,  531   (1894). 


PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 


dielectric  constant  and  the  constants  m,  D,  and  K  for  electrolytes  in 
different  solvents.  So  far  as  possible,  typical  electrolytes  have  been 
chosen,  since,  as  we  have  seen,  the  constants  are  in  general  a  function  of 
the  electrolyte.  We  have  seen,  however,  that  the  typical  electrolytes  be- 
have similarly  in  a  given  solvent,  so  that  a  rough  comparison  may  be 
made  between  the  dielectric  constant  and  the  various  constants  which 
determine  the  form  of  the  conductance  function.  Those  values  of  D 
which  appear  in  parentheses  have  been  calculated  from  the  values  of  P, 
assuming  that  the  value  of  A0  is  proportional  to  the  fluidity  of  the 
solvent.  This  relation  is  not  strictly  true,  particularly  in  the  case  of  the 
inorganic  solvents.  However,  it  unquestionably  gives  the  order  of  mag- 
nitude of  this  constant. 

TABLE  XXXII. 
CONSTANTS  OF  EQUATION  11  AND  DIELECTRIC  CONSTANTS  FOR  VARIOUS  SOLVENTS. 


Solvent 


Solute 


Hydriodic  acid  (C2H5)3N.HC1 

Amylamine AgNO3 

Propionic  acid  LiBr 

Methylaniline   C5H5N .  HBr 

Ethylamine  AgNO3 

Ethylamine NH4C1 

Hydrobromic  acid  (C2H5)3N.HC1 

Aniline   AgNO3 

Aniline   NHJ 

Hydrochtoric  acid (C2H5)3N.HC1 

Acetic  acid  LiBr 

Phenol (CH3)4NI 

Hydrogen  sulfide (C2H5)3N . HC1 

Methylamine    AgNO3 

Ethylenechloride    ( C3H7 )  4NI 

Pyridine  Nal 

Pyridine  KI 

Acetoaceticester NaSCN 

Isoamylalcohol   Nal 

Isoamylalcohol   Lil 

Acetophenone   Nal 

Sulfur  dioxide  KI 

Methylethylketone    Nal 

Isobutylalcohol  Nal 

Acetone    Nal 

Ammonia Nal 

Ammonia AgNO8 

Epichlorhydrin 

Propylalcohol  Nal 

Benzonitrile Nal 


Dielectric 

constant 

m 

29 

1 

58 

4.5 

1 

67 

55 

1 

74 

5.9 

1 

64 

62 

1 

.45 

6.2 

1 

57 

6.3 

1 

51 

7.5 

1 

42 

7.5 

1 

44 

9.5 

1 

42 

9.7 

1 

43 

9.7 

1 

28 

10.0 

1 

58 

10.0 

1 

22 

10.5 

t9 

12.4 

12.4 

* 

15.7 

15.9 

1 

2 

15.9 

t 

16.4 

16.5 

1 

14 

18.4 

B 

18.9 

t 

21.8 

. 

22.0 

0 

83 

22.0 

0 

83 

22.6 

m 

23.0 

0 

75 

26.0 

t 

KX104 


D 

(0.58) 

(6.30) 


(0.22)        2.4X10 

(6.54) 
(0.44) 
(0.51) 
(0.39) 
(0.30) 
0.69  2.8 

(0.30) 

0.30  0.80 

1.45 
13.0 
5.2 
9.5 
5.85 
7.3 
34.0 
8.5 
23.0 
12.0 
39.0 
28.0 
28.0 
48.5 
38.3 
55.0 


0403 
040 


043 
036 


0.208 


The  solvents  are  arranged  in  the  order  of  their  dielectric  constants. 
It  will  be  observed,  in  the  first  place,  that  the  constant  D  is  in  all  cases 
of  the  same  order,  varying  between  0.2  and  0.69  with  a  mean  value  in  the 


FORM  OF  THE  CONDUCTANCE  FUNCTION  91 

neighborhood  of  0.4.  This  constant,  therefore,  is  a  characteristic  prop- 
erty of  the  electrolyte  upon  which  the  solvent  has  only  a  secondary  influ- 
ence. In  this  connection,  it  is  to  be  borne  in  mind  that  various  com- 
plexes may  be  formed  between  an  electrolyte  and  its  solvent,  upon  the 
nature  of  which  complexes  the  constant  D  may  depend.  We  should 
therefore  expect  a  certain  amount  of  variation  in  the  value  of  the  con- 
stant D  for  a  given  electrolyte  in  different  solvents.  Probably  the  change 
in  the  value  of  D  would  be  found  to  be  much  smaller  in  case  the  dielectric 
constant  were  altered,  not  by  a  change  of  the  solvent  medium,  but  by  a 
change  of  the  temperature.  The  constant  ra  is  seen  to  decrease  as  the 
dielectric  constant  increases.  Since  this  constant  is  a  property  of  the 
electrolyte,  as  well  as  of  the  solvent,  it  follows  that  an  exact  comparison 
cannot  be  made.  However,  it  is  clear  that,  for  solvents  of  very  low 
dielectric  constant,  the  value  of  ra  approaches  2,  whereas  for  solvents 
of  very  high  dielectric  constant  the  value  of  ra  is  less  than  unity.  In 
the  case  of  water  ra  appears  to  have  a  value  in  the  neighborhood  of  0.5. 
The  change  in  the  value  of  ra  as  a  function  of  the  dielectric  constant  is 
well  illustrated  in  the  case  of  silver  nitrate  dissolved  in  the  amines.  For 
amylamine,  ethylamine,  aniline,  methylamine,  and  ammonia  the  dielec- 
tric constants  are  respectively  4.5,  6.2,  7.5,  10  and  22,  and  the  values  of 
ra  are  1.67,  1.45,  1.42,  1.22  and  0.83.  It  is  seen  that  throughout  this 
series  of  solvents,  which  are  similar  in  their  constitution,  the  value  of  the 
constant  ra  for  silver  nitrate  decreases  with  increasing  values  of  the 
dielectric  constant. 

The  mass-action  constant  K  decreases  very  rapidly  as  the  dielectric 
constant  decreases.  While  there  are  numerous  transpositions  in  the  order 
of  the  constants,  which  is  to  be  expected,  since  this  constant  is  a  func- 
tion of  the  constitution  of  the  salt  as  well  as  that  of  the  solvent,  never- 
theless, in  a  general  way,  there  can  be  no  question  but  that  the  mass- 
action  constant  K  decreases  as  the  dielectric  constant  decreases.  The 
variation  is  much  more  regular  when  solutions  in  solvents  of  the  same 
type  are  compared.  So,  in  the  case  of  solutions  of  silver  nitrate  in 
ammonia  and  its  derivatives,  the  constants  are  as  follows:  ethylamine, 
2.44  X  lO'8;  methylamine,  0.8  X  10'4;  ammonia,  28  X  10'4.  When  the 
dielectric  constant  falls  below  a  value  of  approximately  10,  the  mass- 
action  constant  for  the  typical  salts  has  reached  a  value  in  the  neighbor- 
hood of  1  X  10-*  and  thereafter  it  falls  off  very  rapidly  with  decreasing 
values  of  the  dielectric  constant.  No  accurate  data  being  available  in 
dilute  solutions  of  solvents  having  a  dielectric  constant  less  than  10,  it  is 
impossible  to  proceed  further  with  the  comparison.  Assuming,  however, 
that  the  conductance  function  holds,  it  is  possible  to  calculate  the  values 


92          PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

of  the  constant  K  if  sufficiently  accurate  data  are  available  at  inter- 
mediate concentrations.  The  value  of  K  for  solutions  in  ethylamine  was 
obtained  in  this  way.  The  extremely  low  value  of  the  constant  will  be 
noted. 

Having  shown  the  relation  between  the  constants  of  the  conductance 
function  and  the  dielectric  constant,  it  will  be  unnecessary  to  give  a 
detailed  list  of  various  solvents  which  have  been  found  to  yield  electro- 
lytic solutions.  The  general  form  of  the  conductance  curve  may  at  once 
be  inferred  from  the  value  of  the  dielectric  constant.  Many  salts  are 
not,  as  a  rule,  soluble  in  solvents  of  low  dielectric  constant.  Neverthe- 
less, certain  typical  salts  form  solutions  with  many  solvents  of  very  low 
dielectric  constant,  as  for  example  silver  nitrate,  which  dissolves  in  amyl 
amine,  which  has  a  dielectric  constant  of  only  4.5.  Such  behavior,  how- 
ever, is  exceptional  and  is  probably  to  be  ascribed  to  the  formation  of 
soluble  complexes  between  the  salt  and  the  solvent.  Various  salts  of 
organic  bases,  however,  as  has  already  been  stated,  are  soluble  in  sol- 
vents of  very  low  dielectric  constant. 

The  question  has  been  raised  as  to  the  influence  of  the  electrolyte  on 
the  dielectric  constant  of  the  medium  in  which  it  is  dissolved.  Walden,17 
who  has  measured  the  dielectric  constants  of  some  non-aqueous  solutions, 
concluded  that  the  dielectric  constant  is  greatly  increased  due  to  the 
addition  of  an  electrolyte  and  has  suggested  that  the  observed  deviations 
of  strong  electrolytes  from  the  simple  mass-action  law  are  due  to  this 
factor.  More  recently,  however,  Lattey  18  has  subjected  the  methods 
of  measuring  the  dielectric  constant  of  electrolytes  to  careful  examina- 
tion and  has  himself  carried  out  measurements  on  numerous  aqueous 
solutions.  He  finds  that  the  dielectric  constant  of  electrolytic  solutions 
is  considerably  lower  than  that  of  the  pure  solvent.  For  example,  for  a 
solution  of  potassium  chloride  in  water  of  concentration  0.00755  normal 
he  obtained  the  value  66.25  as  against  81.45  for  pure  water.  The  dielec- 
tric constant  diminishes  approximately  as  a  linear  function  of  the  con- 
centration and  the  effect  for  different  electrolytes  is  of  the  same  order 
of  magnitude.  Further  investigations  in  this  direction  are  much  needed. 

The  precise  form  of  the  functional  relation  between  the  dielectric 
constant  of  the  solvent  and  the  ionization  of  the  dissolved  electrolyte  is 
unknown.  Walden  19  has  suggested  an  empirical  relation  according  to 
which  the  ionization  of  a  typical  electrolyte  is  the  same  in  different 
solvents  when  the  product  of  the  dielectric  constant  and  the  cube  root 

"Walden,  Bull.  Acad.  St.  Pctersb.  6,  305  and  1055  (1912)  ;  J.  Am.  Chem.  Soc.  35, 
1649  (1913). 

"Lattey,  Phil.  Mag.  1,1,  829   (1921). 

"Walden,  Ztschr.  f.  phys.  Chem.  5k,  228  /1905). 


FORM  OF  THE  CONDUCTANCE  FUNCTION          93 

of  the  dilution  have  the  same  value.  More  recently,  a  number  of  writers 
have  proposed  theories  of  electrolytic  solutions  which  lead  to  Walden's 
relation  as  a  consequence.  Walden  has  made  an  extensive  study  of 
available  data  20  from  which  he  draws  the  conclusion  that  his  relation 
holds  practically  without  exception.  The  theories  in  question  will  be 
discussed  in  another  chapter.  We  shall  here  consider  Walden's  relation 
from  an  experimental  point  of  view  only. 
In  mathematical  terms,  we  have: 

if 

(37)  YI  =  Y2  =  Ya  =,  etc. 
then 

(38)  e^*  =  e2F2*  =  E3F3*  =  ,  etc. 

where  E  is  the  dielectric  constant  of  the  medium  and  V  is  the  dilution 
of  the  solution  of  a  given  electrolyte,  whose  ionization  fulfills  the  con- 
dition 37.  Walden  has  tested  the  relation  by  comparing  the  values  of 
eF*  for  solutions  of  typical  electrolytes  in  different  solvents  and  believes 
to  have  shown  that  this  quantity  is  a  constant  within  the  limits  of  experi- 
mental error  and  minor  variations  due,  perhaps,  to  differences  in  the 
condition  of  the  electrolyte  in  different  media. 

It  is  clear,  from  Equation  38,  that  a  small  variation  in  the  value  of 
the  product  £F*  will  have  as  a  result  a  large  variation  in  the  resulting 
conductance  curve,  since  the  dilution  enters  as  the  cube  root.  Actually 
the  variations  of  the  constants  are  quite  large.  For  example,  at  an 
ionization  of  82%,  the  product  eF*  in  water  has  a  value  of  156,  in 
ammonia  286,  in  isobutylalcohol  333,  and  in  ethylene  chloride  315.  The 
constancy  of  the  values  which  Walden  has  found  is  in  part  due  to  the 
use  of  unreliable  conductance  data  and  in  part  to  the  use  of  A0  values 
which  are  unquestionably  in  error. 

It  is  obvious,  according  to  Equation  38,  that,  if  the  ionization  curve 
is  fixed  for  a  typical  electrolyte  in  one  solvent,  it  is  fixed  for  typical 
electrolytes  in  all  other  solvents.  For  we  have,  considering  solutions  of 
a  given  electrolyte  in  two  different  solvents, 


(39)  or      ^ 

If  F!  is  the  dilution  in  the  first  medium,  at  which  the  ionization  of  the 
electrolyte  is  y,  then  F2,  as  determined  by  Equation  39,  is  the  dilution  in 

»  Walden,  Ztschr.  f.  phys.  Chem.  9$,  263  (1920). 


94          PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

the  second  medium  at  which  the  electrolyte  will  have  the  same  ioniza- 
tion. 

In  the  following  table  are  given  values  of  V  calculated  according  to 
Equation'  39,  at  which  the  ionization  of  typical  electrolytes  is  70%  and 
95%  in  different  solvents,  based  upon  an  aqueous  solution  of  sodium 
chloride  as  reference  medium.  Under  Fobs,  are  given  the  observed  dilu- 
tions at  which  solutions  in  the  various  solvents  have  the  ionization  in 
question. 

TABLE  XXXIII. 

OBSERVED  AND  CALCULATED  VALUES  OF  THE  DILUTION  V  AT  WHICH  TYPICAL  ELECTRO- 
LYTES IN  VARIOUS  SOLVENTS  HAVE  THE  SAME  IONIZATION. 

Ethyl    Epichlor-  Aceto-  Isobutyl-  Ethylene 

Solvent          Water    Alcohol    hydrin  phenone  Pyridine  Ammonia  alcohol    chloride 

Dielectric 

constant    .  81.7  25.6  22.6  18.2  13.0  22.0  18.9  10.5 

A0       108.9  39.42  62.1  33.3  57.0  339.0  12.8  66.7 

Temp 18°  25°  25°  25°  18°  —33.5°  25°  25° 

loniz.  =  70% :  * 

Fobs 1.207        125.9        159.1          320.5         861.0        794.5        1348.0      11290.0 

Fcalc. 1.207         39.2         56.8         109.0         299.0         61.7  97.5         569.0 

loniz.  =  95% : 

Fobs> 181.0      3590.0      3350.0        5970.0      25110.0    11910.0      14620.0 

Fcalc. 181.0      5880.0      8530.0      16300.0      44900.0      9260.0      14600.0 

The  electrolyte  employed  for  comparison  is  sodium  iodide,  except  in  the 
case  of  water,  epichlorhydrin,  ethylene  chloride  and  ammonia,  in  which 
the  electrolytes  were  sodium  chloride,  tetraethylammonium  iodide,  tetra- 
propylammonium  iodide  and  potassium  nitrate,  respectively.  So  far 
as  solutions  in  water  are  concerned,  the  ionization  values  correspond 
very  closely  for  different  binary  electrolytes,  so  that  it  is  a  matter  of 
indifference  whether  one  or  another  typical  binary  electrolyte  is  em- 
ployed as  reference  electrolyte.  At  the  higher  concentrations,  it  is  true, 
the  value  of  y  is  somewhat  lower  for  sodium  chloride  than  for  potassium 
chloride.  However,  this  does  not  affect  the  comparisons  appreciably; 
if  anything,  the  comparison  is  somewhat  more  favorable  with  sodium 
chloride  than  with  potassium  chloride  as  reference  electrolyte. 

If  Equation  38  were  applicable,  the  calculated  values  of  F  should 
everywhere  correspond  with  the  observed  values.  At  an  ionization  of 
70%  the  calculated  values  of  F  are  in  all  instances  too  small.  The  dis- 
crepancy is  greatest  in  the  case  of  ethylene  chloride  at  70%  ionization, 
which,  according  to  calculation,  should  be  569  liters,  whereas  the  meas- 
ured dilution  is  11,290.  In  general,  the  lower  the  dielectric  constant  of 


FORM  OF  THE  CONDUCTANCE  FUNCTION  95 

the  medium,  the  greater  the  discrepancy  between  the  observed  and  cal- 
culated values,  although  there  are  some  marked  exceptions.  Further- 
more, the  order  of  the  deviations  varies  as  the  ionization  of  the  electro- 
lyte varies.  This  is  particularly  noticeable  in  the  case  of  ammonia  and 
isobutyl  alcohol,  where  the  observed  and  calculated  values  very  nearly 
agree  at  95%  ionization,  but  diverge  largely  at  an  ionization  of  70%. 
On  the  other  hand,  in  other  cases,  the  deviation  changes  sign.  For 
example,  at  70%  ionization  the  observed  value  for  ethyl  alcohol  is  125.9 
and  the  calculated  value  39.2,  whereas  at  95%  ionization  the  observed 
value  is  smaller,  being  3590,  and  the  calculated  value  5880. 

That  Walden's  relation  cannot  hold  generally  may  most  readily  be 
shown  by  graphical  means.  If  we  take  logarithms  of  both  sides  of 
Equation  39,  we  have: 

log  V2  — log  Vx  =  31og^. 

82 

If  the  values  of  y  f°r  an  electrolyte  in  different  solvents  are  plotted 
against  values  of  log  V,  then  obviously  for  any  given  value  of  y  the 

abscissas  on  the  curves  will  differ  by  3  log  — .    In  other  words,  the  curve 

£2 

for  an  electrolyte  in  any  one  solvent  may  be  derived  from  that  in  any 
other  solvent  by  merely  displacing  the  curve  along  the  axis  of  log  V  by 

p 

an  amount  equal  to  3  log  — .    An  inspection  of  Figure  3,  where  values 

E2 

of  y  f°r  different  solvents  are  plotted  as  functions  of  log  V,  shows  at 
once  that  this  condition  is  not  fulfilled,  for,  if  the  curve  for  water  were 
displaced  parallel  to  itself,  it  would  not  coincide  with  the  curves  for 
solutions  of  typical  electrolytes  in  other  solvents,  such  as  ethyl  alcohol, 
ammonia  and  ethylene  chloride.  Indeed,  in  order  to  test  the  applicability 
of  Walden's  relation  it  is  not  even  necessary  to  know  the  value  of  A0, 

since  it  follows  readily  from  Equation  39  and  from  the  equation  y  =—r- 

A0 

that  if  the  conductances  themselves  are  plotted  as  functions  of  log  V,  it 
must  be  possible  to  derive  the  curve  for  an  electrolyte  in  any  one  solvent 
from  that  in  any  other  solvent  by  displacing  the  curve  parallel  to  itself 
in  some  direction,  this  direction  being  determined  by  the  values  of  A0 
and  of  the  dielectric  constant  8.  Those  familiar  with  the  properties  of 
electrolytic  solutions  will  at  once  recognize  that  this  condition  is  not 
fulfilled. 

Actually,  it  is  not  to  be  expected  that  any  simple  relation  will  exist 
between  the  ionization  y  and  the  dielectric  constant  of  the  solvent,  for, 


96          PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

as  we  have  seen,  the  value  of  y  is  expressed  approximately  as  a  function 
of  the  concentration  by  means  of  Equation  11.  As  was  pointed  out 
above,  the  constant  D  is  practically  independent  of  the  dielectric  con- 
stant, while  ra  increases  and  K  decreases  with  increasing  values  of  this 
constant.  As  a  result,  the  relative  ionization  of  an  electrolyte  in  two 
solvents  will  vary  with  the  concentration  in  a  more  or  less  complex 
manner,  and  in  two  solvents  the  order  of  the  ionization  values  may  be 
reversed  as  the  concentration  changes. 

The  important  conclusion  to  be  drawn  from  the  behavior  of  solutions 
of  electrolytes  in  different  solvents  is  that  the  conductance  function  is 
of  the  same  general  form  in  all  solvents.  A  single  empirical  equation 
is  capable  of  expressing  the  relation  between  the  conductance  and  the 
concentration  in  all  cases,  practically  within  the  limits  of  experimental 
error.  Whether  or  not  this  equation  represents  precisely  the  relation 
between  the  conductance  and  the  concentration  is  relatively  unimportant, 
so  long  as  the  deviations  from  this  equation  show  no  decided  systematic 
trend.  In  aqueous  solutions,  the  weak  electrolytes  follow  the  mass- 
action  law  in  conformity  with  the  ionic  theory.  The  strong  electrolytes, 
however,  do  not  fulfill  this  condition.  It  follows  from  the  foregoing  con- 
siderations that  the  conductance  curve  for  strong  electrolytes  in  water  dif- 
fers from  that  of  electrolytes  in  other  solvents  only  as  regards  magnitude 
of  the  observed  effects  and  not  as  regards  the  nature  of  the  phenomena 
involved.  Any  theory  which  has  to  account  for  the  relation  between  the 
conductance  and  the  concentration  of  electrolytes  in  water  must  equally 
account  for  the  relation  between  these  quantities  in  non-aqueous  solvents. 

Various  theories  have  been  proposed  to  account  for  the  change  of 
the  equivalent  conductance  as  a  function  of  the  concentration  in  the  case 
of  strong  electrolytes.  The  simplest  of  these  is  that  the  degree  of  ioniza- 
tion is  actually  measured  by  the  conductance  ratio,  in  which  case  it  is 
necessary  to  account  for  the  change  in  ionization  as  a  function  of  the 
concentration.  Unfortunately,  a  general  theory  of  other  than  dilute 
solutions  does  not  exist  at  the  present  time.  A  comprehensive  method 
of  treating  concentrated  solutions  is  therefore  lacking.  The  problem  of 
equilibrium  in  a  system  of  charged  particles  has  not  been  solved,  and  the 
question  therefore  remains  open  as  to  whether  or  not  the  change  in 
ionization  may  be  accounted  for.  On  the  other  hand,  the  assumption 
may  be  made  that  the  speed  of  the  ions  changes  as  a  function  of  the 
concentration,  as  a  consequence  of  which  the  conductance  ratio  does  not 
correctly  measure  the  degree  of  ionization.  Certain  writers  have  as- 
sumed that  typical  electrolytes  are  completely  ionized  in  solution  and 
that  consequently  the  change  in  the  conductance  is  due  entirely  to  a 


FORM  OF  THE  CONDUCTANCE  FUNCTION  97 

change  in  the  speed  of  the  carriers.  It  should  be  stated,  however,  in 
this  connection,  that  no  theory  has  thus  far  been  proposed  which  ade- 
quately accounts  for  the  change  in  the  carrying  capacity  of  the  ions  as 
a  function  of  the  concentration,  particularly  in  solvents  of  low  dielectric 
constant.  Any  such  theory  must  not  only  account  for  an  initial  diminu- 
tion in  the  speed  of  the  ions,  but  it  must  also  account,  in  many  cases, 
for  a  subsequent  increase  in  the  speed  with  increasing  concentration. 
In  fact,  such  a  theory  must  account  for  the  various  forms  of  the  con- 
ductance curves  in  different  solvents  and  for  the  change  in  the  form  of 
the  curves  as  the  condition  of  the  solvent  is  altered.  Incidentally,  it  is 
to  be  noted  that  the  order  of  the  changes  in  the  speed  of  the  ions  on 
this  assumption  is  very  great.  It  is  true  that,  in  aqueous  solutions,  the 
speed  does  not  vary  greatly  from  the  most  dilute  solutions  up  to  normal 
concentration,  but  in  solutions  in  solvents  of  low  dielectric  constant  it  is 
not  only  necessary  to  account  for  a  decrease  in  speed  but  in  many  cases 
for  an  increase  in  speed  which,  over  a  limited  range  of  concentration,  is, 
at  times,  as  great  as  a  thousandfold.  It  seems  very  difficult  to  account 
for  a  change  of  speed  of  this  magnitude  on  the  basis  of  our  present 
knowledge  of  the  properties  of  the  carriers  in  different  media.  In  this 
connection  it  should  be  borne  in  mind  that,  superimposed  on  these 
hypothetical  changes  in  the  speed  of  the  ions,  there  is  a  change  due  to 
the  viscosity  of  the  solution  which  effect  appears  in  every  respect  to 
be  normal  in  character.  Furthermore,  solutions  of  weak  electrolytes, 
both  in  water  and  non-aqueous  solvents,  conform  to  the  mass-action  law 
up  to  fairly  high  concentrations.  If  the  speed  of  the  ions  changes  with 
the  concentration,  then  such  a  simple  relation  is  not  to  be  expected. 

A  third  hypothesis  has  been  proposed,  namely:  that  the  ionization 
reaction  differs  from  that  which  is  commonly  assumed.  Certain  writers 
have  made  the  assumption  that,  in  non-aqueous  solutions,  the  electrolyte 
is  associated,  the  association  changing  with  concentration,  and  that  only 
the  associated  molecules  are  capable  of  ionization.  They  assume,  for 
example,  in  the  simplest  case,  that  the  following  reactions  take  place: 

=  (MX)2 


As  the  concentration  increases,  the  amount  of  the  polymer  increases  and 
this  increase  might  be  sufficient  to  provide  for  an  actual  increase  in  the 
number  of  ions  present.  If  this  hypothesis  is  correct,  the  current  in  such 
solutions  is  carried  chiefly  by  complex  ions  and  consequently  transfer- 
ence numbers  in  such  solutions  should  be  abnormal.  Reliable  trans- 
ference numbers  in  solvents  of  low  dielectric  constant  are  not  available, 


98         PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

but  from  the  data  for  solvents  of  somewhat  higher  dielectric  constant 
it  may  be  inferred  that  the  transference  numbers  are  approximately 
normal.  Furthermore,  since  it  appears  that  the  deviations  from  the 
mass-action  law  in  aqueous  solutions  are  of  the  same  character  as  in 
non-aqueous  solutions,  it  follows  that  similar  intermediate  ions  would 
have  to  be  assumed  to  be  present  in  solutions  of  the  strong  binary  elec- 
trolytes in  water.  If  such  were  the  case,  not  only  should  the  trans- 
ference numbers  be  abnormal,  but  they  should  vary  as  a  function  of  the 
concentration.  Now,  while  it  is  true  that  many  transference  numbers 
do  vary  with  the  concentration,  a  considerable  variation  takes  place  only 
at  relatively  high  concentrations,  and  only  at  such  concentrations  where 
the  viscosity  of  the  solution  has  increased  sufficiently  to  materially  affect 
the  motion  of  the  ions  through  the  solution.  It  would  seem  that  trans- 
ference measurements  should  yield  data  corroborating  this  last  hypothesis 
if  it  were  correct.  So  far  as  available  data  are  concerned,  the  hypothesis 
is  not  substantiated. 

4.  The  Form  of  the  Conductance  Curve  in  Dilute  Aqueous  Solu- 
tions. The  applicability  of  the  conductance  function  to  aqueous  solu- 
tions is  uncertain.  That  the  Storch  equation  holds  approximately  for 
aqueous  solutions  at  higher  concentrations  has  long  been  known.  In 
the  case  of  Equation  11  this  would  yield  for  m  values  of  approximately 
0.5,  and  for  D  values  in  the  neighborhood  of  2.  With  such  large  values 
of  the  constant  D  and  small  values  of  the  constant  m,  it  becomes 
very  difficult  to  determine  the  value  of  the  constant  K.  At  concentra- 
tions sufficiently  low,  so  that  the  effect  of  the  D  term  might  be  neglected, 
the  ionization  is  so  nearly  complete  that  it  becomes  practically  impos- 
sible to  demonstrate  whether  or  not  the  mass-action  law  is  approached 
as  a  limiting  form.  Kraus  and  Bray  have  shown  that  Equation  11  may 
be  applied  with  considerable  exactitude  to  solutions  in  water  up  to  10~3 
normal,  provided  a  value  of  A0  is  chosen  which  is  lower  than  the  experi- 
mentally determined  values  of  the  equivalent  conductance  at  very  low 
concentrations.  More  recently,  Washburn  and  Weiland21  have  con- 
cluded from  their  very  accurate  conductance  measurements  on  KC1  up 
to  2  X  10~5  normal  that  the  mass-action  law  is  actually  approached  as 
a  limit.  Their  results,  however,  do  not  appear  to  be  conclusive,  since, 
in  extrapolating  for  the  value  of  A0,  they  assume  the  mass-action  law 
to  hold.22  If  the  mass-action  constant  is  calculated  with  a  value  of  A0 
based  on  the  assumption  that  the  mass-action  law  holds,  then  the  results 
must  necessarily  conform  to  the  assumption  made.  The  curve  obtained 

"Washburn  and  Weiland,  J.  Am.  Cher*.  Soc.  W,  106  (1918). 
»» Kraus,  J.  Am.  Cfhem.  Soc.  4%,  1  (1920). 


FORM  OF  THE  CONDUCTANCE  FUNCTION 


99 


is  shown  in  Figure  14,  in  which  values  of  the  mass-action  function  K' 
are  plotted  against  those  of  the  concentration.  The  form  of  this  function 
is  entirely  different  from  that  which  has  been  found  to  hold  in  solutions 
in  non-aqueous  solvents  and  it  is  obvious,  moreover,  that  the  function  is 
a  comparatively  complex  one.  At  higher  concentrations,  and  practically 
down  to  1.5  X  10"4  normal,  the  K',  C-curv£  is  everywhere  concave 
toward  the  axis  of  concentrations.  At  this  low  concentration,  however, 
the  curve  changes  its  form,  and  approaches  a  value  asymptotic  to  a  line 
parallel  to  the  axis  of  concentrations.  In  order  to  establish  the  mass- 
action  law  as  a  consequence  of  experimental  observations  it  must  be 


Concentration  X 


FIG.  14.    Showing  Variation  of  K'  with  Concentration  for  Aqueous  Solutions  of 
KC1  at  18°  According  to  Washburn. 

shown  that,  over  a  measurable  concentration  interval,  points  on  the  curve 
necessarily  lie  upon  a  horizontal  straight  line.  As  this  has  not  been 
done,  it  is  evident  that  Washburn's  conclusions  remain  in  doubt. 

The  manner  in  which  the  curve  for  the  mass-action  function  ap- 
proaches the  axis  depends  upon  the  value  of  the  constant  m  in  the 
general  equation.  For  values  of  m  greater  than  unity,  the  curve  ap- 
proaches the  axis  asymptotic  to  a  line  parallel  to  the  axis  of  concen- 
trations; while  for  values  of  m  less  than  unity,  it  approaches  the  axis 
asymptotic  to  the  axis  of  K' .  In  the  case  of  water,  therefore,  for  which 
the  value  of  m  appears  to  be  less  than  unity,  we  should  expect  that  the 
K!  curve  would  be  everywhere  concave  toward  the  axis  of  concentrations. 


100        PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

The  conductance  of  potassium  chloride  solutions  between  the  concen- 
trations of  10'*  and  2  X  10~5  normal  may  be  represented  well  within  the 
limits  of  experimental  error,  by  means  of  the  Equation  11 23  in  which 
the  constants  have  the  value:  ra  =  0.52,  D  —  1.703,  A0  =  129.9,  and 
K  =  10  X  10-4.  Washburn's  value  for  K  is  200  X  lO'4.  Actually,  this 
represents  an  upper  probable  limit  for  the  value  of  the  constant  K. 
The  value  10  X  10~*  would  appear  to  be  too  small.  Salts  in  the  alcohols 
have  values  of  the  mass-action  constant  considerably  greater  than  this. 
Since,  in  general,  the  value  of  the  mass-action  constant  increases  with 
the  dielectric  constant,  we  should  expect  that  the  value  of  this  constant 
in  the  case  of  aqueous  solutions  would  be  greater  than  in  the  alcohols. 
It  should  be  noted,  however,  that  the  experimental  results  might  still 
be  represented  within  the  limits  of  experimental  error  if  a  value  con- 
siderably greater  than  10  X  10~4  were  assumed  for  the  mass-action  con- 
stant. It  is  possible,  therefore,  that  the  salts  in  water  may  have  a  value 
of  the  mass-action  constant  as  high  as  100  X  10'*.  On  the  other  hand, 
so  far  as  the  actual  data  are  concerned,  it  cannot  be  definitely  demon- 
strated that  the  mass-action  law  is  approached  as  a  limiting  form  in 
aqueous  solutions  of  strong  electrolytes.  Even  the  value  of  200  X  10~4 
for  potassium  chloride  appears  to  be  distinctly  lower  than  the  value  of 
the  constants  for  certain  much  weaker  electrolytes  in  aqueous  solution, 
as,  for  example,  acids  of  intermediate  strength. 

In  the  case  of  the  strong  acids  and  bases,  sufficient  data  are  not 
available  to  determine  the  order  of  magnitude  of  the  limit  which  the 
function  K'  approaches.  If  the  data  relating  to  hydrochloric  acid  are 
correct,  the  ionization  of  this  acid  in  a  10~4  normal  solution  is  as  low 
as  that  of  potassium  chloride  at  the  same  concentration,  assuming  that 
the  value  of  A0  for  hydrochloric  acid  is  380.0.  Actually  this  value  of 
A0  is  somewhat  too  low  and  the  value  382.0  is  probably  more  nearly 
correct.  It  would  appear,  therefore,  that  the  strong  acids  may  approach 
a  value  of  the  mass-action  constant  as  low  or  lower  than  that  of  the 
salts;  or,  in  other  words,  values  lower  than  200  X  10~4.  No  data  are 
available  from  which  the  ionization  of  the  strong  bases  may  be  calculated 
at  low  concentrations. 

The  limiting  values  which  the  ionization  constants  of  the  strong  acids 
and  bases  approach  at  low  concentrations  is  of  considerable  practical 
importance,  since  the  hydrolysis  of  salts  depends  upon  the  relative  values 
of  these  constants  and  that  of  water.  If  the  values  which  the  mass- 
action  constants  of  the  bases  and  acids  approach  at  low  concentrations 
are  sufficiently  small,  then  the  salts  of  these  acids  and  bases  will  be 

»Kraus,  Joe.  cit. 


FORM  OF  THE  CONDUCTANCE  FUNCTION         101 

hydrolyzed  to  an  appreciable  extent  at  very  low  concentrations.  In 
case  the  limits  approached  differ  for  the  acids  and  the  bases,  the  meas- 
urement of  the  conductance  of  very  dilute  salt  solutions  will  be  affected 
by  hydrolysis.  It  appears  not  impossible  that  the  bases  may  approach 
values  of  the  mass-action  constant  lower  than  those  of  the  acids.  In 
liquid  ammonia  solutions  the  ionization  constants  of  the  bases  are  much 
lower  than  those  of  the  acids.  We  might,  therefore,  expect  that  at  con- 
centrations approaching  10~5  normal  the  conductivity  of  the  salt  might 
be  appreciably  affected  by  hydrolysis.  This  is  almost  certainly  the  case 
with  silver  nitrate.  The  ionization  constant  of  this  base  is  approxi- 
mately 2.5  X  10~4  at  25°.  This  value  is  based  on  the  solubility  of  a 
saturated  solution  of  silver  oxide  in  water  whose  ionization  has  been 
determined  to  be  approximately  0.64.  At  10~3  normal  the  conductance 
of  the  silver  nitrate  solution  would  be  affected  to  the  extent  of  0.7  per 
cent  due  to  hydrolysis.  Until  more  accurate  data  are  available  on  the 
ionization  of  the  strong  acids  and  bases  at  low  concentrations,  the  inter- 
pretation of  conductance  measurements  with  salts  at  low  concentrations 
remains  in  doubt. 

5.  Solutions  of  Formates  in  Formic  Acid.  It  is  evident,  from  the 
considerations  of  the  foregoing  sections,  that,  as  the  concentration  of  an 
electrolyte  increases,  the  value  of  the  function  K'  increases.  In  other 
words,  as  the  concentration  of  the  electrolyte  increases,  the  conductance 
falls  less  rapidly  than  required  by  the  simple  mass-action  relation.  As 
we  have  seen,  if  the  simple  mass-action  law  holds,  then  a  plot  of  the 
reciprocal  of  the  equivalent  conductance  against  the  specific  conductance, 
or  the  ion  concentration,  yields  a  linear  relation  between  the  experi- 
mentally determined  points.  Deviations  from  the  mass-action  law  are 
then,  obviously,  such  that  at  high  concentrations  the  points  diverge  from 
a  straight  line  toward  the  axis  of  specific  conductances.  In  general, 
therefore,  these  curves  are  concave  toward  the  axis  of  specific  con- 
ductances. There  are  indeed  a  few  cases  in  which  the  curves  are  convex 
toward  the  axis  of  specific  conductances,  or,  in  other  words,  in  which 
the  deviations  from  the  mass-action  relation  are  in  the  opposite  direction. 
This  has  been  found  to  be  the  case  with  aqueous  solutions  of  certain 
weak  organic  acids  whose  viscosity  is  very  high.  Presumably  this  form 
of  the  curve  is  due  to  the  rapidly  increasing  viscosity  of  the  solution  at 
higher  concentration.  The  same  form  of  curve  has  been  found  by 
Schlesinger  and  his  associates  for  solutions  of  formates  in  formic  acid.24 

•*  Schlesinger  and  Calvert,  J.  Am.  Chem.  8oc.  S3,  1924  (1911)  ;  Schlesinger  and 
Martin,  J.  Am.  Chem.  Soc.  36,  1589  (1914)  ;  Schlesinger  and  Coleman,  J.  Am.  Chem.  Soc.  38 
271  (1916)  ;  Schlesinger  and  Mullinix,  J.  Am.  Chem.  Soc.  41,  72  (1919)  ;  Schlesinger  and 
Reed,  J.  Am.  Chem.  Soc.  41,  1921  (1919)  ;  Schlesinger  and  Bunting,  J.  Am.  Chem.  Soc.  11. 
1934  (1919). 


102        PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

According  to  Schlesinger,  solutions  of  the  formates  in  formic  acid 
present  an  anomaly  in  that,  while  they  are  highly  ionized,  differing  but 
little  in  this  respect  from  aqueous  solutions,  the  simple  law  of  mass-action 
is  obeyed  up  to  concentrations  as  high  as  0.3  normal.  If  this  interpreta- 
tion is  correct,  it  will  be  necessary  to  revise  all  commonly  accepted  notions 
relative  to  the  causes  underlying  the  deviations  from  the  simple  mass- 
action  law,  since  in  these  solutions  we  would  have  a  case  in  which  the 
law  of  mass-action  is  obeyed  up  to  high  concentration  for  solutions  of 
strong  electrolytes.  We  may,  therefore,  examine  the  results  obtained 

Specific  Conductance  of  Sodium  Acetate  in  Water. 

10.  20.  30.  40.  SO  60.  70 

.029 


0.  S.  10.  15.  ZO.  £S.  30.  35. 

Specific  Conductance  of  Sodium  Formate  in  Formic  Acid. 
FIG.  15.    Comparison  of  Conductance  Curves  in  Formic  Acid  and  in  Water. 

in  formic  acid  with  some  care  in  order  to  determine  whether  or  not  solu- 
tions in  this  solvent  may  be  brought  into  line  with  solutions  in  other 
solvents. 

It  is  at  once  apparent  that  measurements  with  solutions  in  formic 
acid  may  lead  to  difficulties  of  interpretation,  owing  to  the  fact  that  the 
conductance  of  the  pure  solvent  is  very  high.  It  is  not  possible  to 
carry  the  measurements  to  very  low  concentrations ;  and  if  such  measure- 
ments are  carried  out,  the  results  will  always  be  more  or  less  in  doubt. 
In  Figure  15,  the  upper  curve  represents  a  plot  of  I/A  against  the 
specific  conductance  for  solutions  of  sodium  formate  in  formic  acid, 
according  to  Schlesinger.  It  will  be  observed  that,  between  a  concen- 
tration of  C  =  0.0667  and  C  =  0.297,  the  points  lie  upon  a  straight  line 
within  the  limits  of  experimental  error.  At  lower  concentrations  the 
curve  deviates  from  a  straight  line,  being  concave  toward  the  axis  of 


FORM  OF  THE  CONDUCTANCE  FUNCTION  103 

ion  concentrations,  while  at  higher  concentrations  it  is  convex  toward 
this  axis;  in  other  words,  the  experimentally  determined  points  lie  upon 
a  curve  which  has  an  inflection  point  somewhere  between  the  concentra- 
tions given  above,  probably  in  the  neighborhood  of  0.1  normal.  Schles- 
inger  is  inclined  to  attribute  the  deviation  of  the  points  in  the  more 
dilute  solutions  to  the  presence  of  impurities.  So  far  as  the  conductance 
of  the  solvent  is  concerned,  since  sodium  formate  has  an  ion  in  common 
with  formic  acid,  it  is  to  be  expected  that  the  ionization  of  formic  acid 
itself  will  be  repressed  by  sodium  formate,  so  that  the  conductance  of  the 
pure  solvent  itself  will  not  enter.  He  believes,  however,  that  there  are 
present  in  the  solvent  impurities,  as  a  result  of  which  the  measured  con- 
ductance is  higher  than  that  due  to  the  electrolyte.  On  the  other  hand, 
it  is  known  that  the  salts  of  the  fatty  acids  yield  ions  which  move  very 
slowly  and  whose  solutions  exhibit  an  extremely  high  viscosity.  The 
form  of  the  curve  in  the  case  of  the  formates  in  formic  acid  is  similar 
to  that  of  certain  acids  in  water.  Further  light  may  be  thrown  upon 
this  question  by  considering  the  conductance  curves  of  salts  of  organic 
acids  in  water,  whose  solutions  likewise  exhibit  a  high  viscosity.  The 
lower  curve  in  Figure  15  represents  a  plot  of  I/ A  against  the  specific 
conductances  for  sodium  acetate  in  water  at  18°.  An  inspection  of  the 
figure  shows  at  once  that  the  curve  for  sodium  acetate  in  water  is  in  all 
respects  similar  to  that  of  sodium  formate  in  formic  acid.  Between  the 
concentrations  0.1  and  0.5  normal,  the  points  lie  upon  a  straight  line 
within  the  limits  of  experimental  error.  In  the  more  dilute  solutions, 
the  experimentally  determined  points  lie  upon  a  curve  concave  toward 
the  axis  of  concentrations  and  in  the  more  concentrated  solutions  on  a 
curve  convex  toward  this  axis.  In  the  case  of  sodium  formate  in  formic 
acid,  the  concentration  interval  over  which  the  points  lie  upon  a  straight 
line  is  0.0667  to  0.297,  corresponding  to  a  concentration  ratio  of  4.45, 
while  in  the  case  of  sodium  acetate  in  water  the  corresponding  concen- 
tration interval  is  0.1  normal  to  0.5  normal,  whose  ratio  is  5.0.  If  we 
hold  that  the  law  of  mass-action  applies  to  solutions  of  sodium  formate 
in  formic  acid,  we  might  equally  well  hold  that  this  law  applies  to  solu- 
tions of  potassium  acetate  in  water.  Our  knowledge  of  the  behavior  of 
aqueous  solutions,  however,  is  such  that  it  is  at  once  evident  that  the 
linear  form  of  the  curve  between  0.1  and  0.5  normal  is  due  to  the  fact 
that,  owing  to  the  high  viscosity  of  the  solutions  at  higher  concentra- 
tions, the  conductance  as  measured  is  smaller  than  it  otherwise  would  be. 
On  the  other  hand,  in  the  more  dilute  solutions  the  form  of  the  curve 
in  the  case  of  sodium  acetate  is  entirely  similar  to  that  of  other 
binary  electrolytes  in  water.  It  is  difficult,  therefore,  to  escape  the  con- 


104        PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

elusion  that  in  the  case  of  solutions  of  the  formates  in  formic  acid, 
likewise,  the  approximately  linear  form  of  the  curve  over  a  limited  con- 
centration interval  is  due  to  the  existence  of  an  inflection  point  and  that 
the  causes  underlying  the  course  of  the  curve  are  the  same  as  those  in 
solutions  of  sodium  acetate  in  water.  It  appears  probable,  therefore, 
that  solutions  of  the  formates  in  formic  acid  do  not  constitute  an  excep- 
tion to  the  well-known  behavior  of  strong  electrolytes  in  solvents  of  high 
dielectric  constant.  From  this  point  of  view  these  solutions  are  normal 
in  their  behavior. 

6.  The  Behavior  of  Salts  of  Higher  Type.  Up  to  this  point,  the 
electrolytes  considered  have  been  of  the  binary  type.  In  the  case  of 
salts  of  higher  type  the  interpretation  of  conductance  measurements 
becomes  much  more  difficult  and  uncertain,  since  it  is  possible,  and  even 
probable,  that  ionization  may  take  place  in  several  stages,  as  indeed  it 
does  in  the  case  of  weak  acids  and  bases.  For  example,  a  salt  of  the 
type  MX2  may  ionize  according  to  the  equations: 

MX2  =  MX+  +  X- 

MX+  =  M++  +  X- 
MX2  =  M++  +  2X-. 

If  ionization  takes  place  only  according  to  the  last  equation,  then  the 
degree  of  ionization  may  be  calculated  from  conductance  measurements. 
But  if  ionization  takes  place  according  to  the  first  two  equations,  then  it 
is  not  possible  to  determine  the  number  of  carriers  in  the  solution  at  a 
given  concentration.  In  the  case  of  weak  dibasic  acids,  ionization  often 
takes  place  according  to  the  first  two  equations,  the  constants  of  the 
two  reactions  being  such  that  one  reaction  is  practically  completed  before 
the  other  reaction  has  begun.  With  salts  this  does  not  appear  to  be 
the  case. 

In  any  case,  if  the  concentration  is  sufficiently  low,  we  should  expect 
that,  ultimately,  there  would  be  present  in  the  solution  only  the  ions  M++ 
and  X-.  Since  the  ion  M++  carries  two  charges,  its  carrying  capacity 
will  be  approximately  twice  as  great  as  that  of  an  ion  carrying  only  a 
single  charge.  The  molecular  conductance  of  such  an  electrolyte  should 
therefore  approach  a  value  approximately  twice  that  of  a  binary  electro- 
lyte, or  its  equivalent  conductance  should  approach  a  value  of  the  same 
order  as  that  of  binary  electrolytes.  An  examination  of  the  conductances 
given  in  Table  III  indicates  that  this  is  the  case.  The  limiting  value 
of  the  equivalent  conductance  for  salts  of  different  type  is  throughout 
of  the  same  order,  and  we  may  conclude,  therefore,  that  at  low  concen- 


FORM  OF  THE  CONDUCTANCE  FUNCTION         105 

trations  the  carrying  capacity  of  an  electrolyte  is  determined  by  the 
number  of  charges  associated  with  the  ionic  constituents. 

In  solutions  of  salts  of  the  type  of  copper  sulphate,  reaction  may  take 
place  according  to  the  equation: 

CuSO,  =  Cu+*  +  S04-. 

This  reaction  is  a  binary  one,  similar  to  that  of  the  binary  salts,  but 
the  molecular  conductance  of  such  a  salt  should  be  twice  that  of  a  binary 
salt.  Such  has  been  found  to  be  the  case. 

This  behavior  of  salts  of  higher  type  appears  to  be  quite  general 
and  is  not  confined  to  aqueous  solutions.  In  Table  XXXIV  are  given 
conductance  values  for  solutions  of  strontium  and  barium  nitrates  in 
ammonia.  It  will  be  observed  that  in  both  cases  the  limiting  value  of 
the  molecular  conductance  is  much  higher  than  that  of  binary  electro- 
lytes and  is,  in  fact,  approximately  twice  that  of  these  electrolytes.  We 
may  assume,  therefore,  that  in  these  solutions  we  have  ultimately  a 
reaction  corresponding  to  the  type: 


It  is  apparent,  however,  that  at  a  given  concentration  the  number  of 
carriers  present  in  solutions  of  these  electrolytes  is  much  lower  than  it  is 
in  solutions  of  typical  binary  electrolytes.  Owing  to  the  low  value  of 
the  ionization,  the  values  of  A0  for  electrolytes  of  this  type  have  not  been 
determined  with  any  degree  of  certainty. 

TABLE  XXXIV. 
CONDUCTANCE  OF  TERNARY  SALTS  IN  NH3  AT  —  33°. 

Sr(N03)225  Ba(N03)226 

V  Arnol  V  Amol 

286.2  145.0  91.1  101.3 

1283.0  207.0  1407.0  2006 

5441.0  275.8  14950.0  3194 

20360.0  359.3  58750.0  4225 

61660.0  449.0  116500.0  4985 

151100.0  514.2 

Similar  results  have  been  obtained  with  solutions  of  ternary  electro- 
lytes in  various  other  solvents,  such  as  acetone,  pyridine,  and  the  like. 
In  many  cases,  however,  the  solubility  of  these  salts  is  relatively  low 
and  their  ionization  at  ordinary  concentrations  is  often  extremely  small. 
They  do  not,  therefore,  lend  themselves  to  a  quantitative  study  of  the 

"Franklin  and  Kraus,  Am.  Chem.  J.  23,  292   (1900) 

38  Franklin  and  Kraus,  J.  Am.  Chem.  Hoc.  27,  200  (1905). 


106       PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

relation  between  the  conductance  and  the  concentration.  In  the  case 
of  aqueous  solutions,  however,  sufficient  data  are  available  to  make  it 
possible  to  obtain  a  general  notion  as  to  the  manner  in  which  the  con- 
ductance varies  as  a  function  of  concentration.  Assuming  a  reaction  of 
the  type 

MX2  =  M-  +  2X-, 

and  assuming  the  mass-action  law  to  apply,  we  obtain  the  equation: 


In  Table  XXXV  are  given  values  of  the  function  K'  calculated 
according  to  the  above  equation  at  a  series  of  concentrations  for  calcium 
chloride  dissolved  in  water  at  18°. 

TABLE  XXXV. 

VALUES  OP  THE  MASS-ACTION  FUNCTION  FOR  CaCl2  SOLUTION 
IN  H20  AT  18°. 


C  ....   ID'3      5X10-3     2X10-2      10'1      5X10-1 

.954  .910  .849  .764  .686 

1.88X10'5        1.7X10'4        1.62X10'3        1.88X10'2        2.6X10'1 


I  v:.: 


It  will  be  observed  that  the  mass-action  function  for  this  salt  increases 
very  greatly  with  the  concentration.  On  the  whole,  the  increase  is  much 
more  marked  than  it  is  for  binary  electrolytes.  The  value  of  the  func- 
tion, moreover,  is  much  lower  throughout  than  it  is  for  solutions  of  binary 
electrolytes.  At  5  X  10'1  normal  the  value  of  K'  is  only  0.26,  which  is 
approximately  one-half  that  of  potassium  chloride,  while  at  10'3  normal 
the  value  is  1.88  X  10~5.  The  mass-action  function,  therefore,  falls  off 
very  rapidly  as  the  concentration  decreases.  In  the  case  of  copper  sul- 
phate solutions  we  have  the  equation: 


Values  of  the  mass-action  function  for  this  electrolyte  at  different  con- 
centrations are  given  in  Table  XXXVI.  At  higher  concentrations  the 
value  of  the  function  K'  for  this  salt  is  smaller  than  that  for  calcium 
chloride,  but  the  constant  decreases  much  less  rapidly  as  the  concentra- 
tion decreases  and  at  lower  concentration  the  value  of  the  function  is 
much  greater  than  that  of  calcium  chloride.  On  the  whole,  the  function 
appears  to  undergo  a  smaller  change  with  the  concentration  in  the  case  of 
copper  sulphate  than  in  that  of  uni-univalent  electrolytes.  However,  it 


FORM  OF  THE  CONDUCTANCE  FUNCTION  107 

is  to  be  borne  in  mind  that  the  value  of  A0  for  this  electrolyte  is  much 
less  certain  than  that  for  the  uni-univalent  salts. 

TABLE  XXXVI. 

VALUE  OF  THE  MASS-  ACTION  FUNCTION  FOR  CuS04  IN  H20  AT  18°. 

C  .....       10-3  5X10'3  2X10'2  lO'1  1.0 

y%....       86.2  70.9  55.0  39.6  30.9 

K  .....  5.4X10'3        8.6X10-3        1.34X10'2        2.6X10'2        1.38X10"1 

As  the  salts  become  more  complex,  the  value  of  the  mass-action  func- 
tion becomes  smaller  and  decreases  more  rapidly  as  the  concentration 
decreases.  For  potassium  ferrocyanide,  assuming  the  reaction  equation: 

K4FeCN6  =  4K+  +  FeCN6~~, 
the  mass-action  function  has  the  form: 


CU-Y) 

Values  of  the  function  at  different  concentrations  are  given  in  Table 
XXXVII  for  this  salt,  as  well  as  for  lanthanum  sulphate.  The  constant 
for  the  ferrocyanide  is  throughout  small  and  at  low  concentrations 
approaches  values  of  an  entirely  different  order  of  magnitude  from  that 
at  the  higher  concentrations.  In  the  case  of  lanthanum  sulphate,  the 
change  in  the  constant  is  even  more  pronounced,  as  may  be  seen  from 
an  inspection  of  the  table. 

TABLE  XXXVII. 

VALUES  OF  THE  MASS-  ACTION  FUNCTION  OF  AQUEOUS  SALT  SOLUTIONS. 

K4FeCN6 

C      2X10-3       1.25X10'2    5.0X10'2      1.0X10'1      3.0X10'1      4.0X10'1 
y%     85.8  71.0  68.7  53.2  48.8  45.3 

K    .52X10'10     1.5X108     1.03X10-6  0.920X10'5    4.33X10'4  0.925X10'3 

La2(S04)3 

C  ...........       2X10'3  10'2  5X10'2 

Y%  .........        51.4  33.9  26.2 

K   ..........   1.28X10'12        0.67X10-10        1.03X10'8 

It  is  obvious  that,  in  solutions  of  electrolytes  of  higher  type,  the 
mass-action  function  varies  the  more  the  higher  the  type  of  the  salt. 
The  value  which  the  function  appears  to  approach  at  very  low  concen- 


108        PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

trations  becomes  extremely  small  and  it  is  uncertain  whether  or  not  the 
function  approaches  a  limiting  value  other  than  zero.  The  interpreta- 
tion of  the  results,  moreover,  is  rendered  uncertain  owing  to  the  possible 
formation  of  intermediate  ions.  It  might  be  expected,  however,  that, 
in  the  limit,  the  intermediate  ions  will  disappear  and  the  function  will 
correspond  to  the  usual  mass-action  function. 

Although  the  curves  become  quite  complex  for  salts  of  higher  type, 
it  appears,  nevertheless,  that  the  conductance  curves  at  higher  concen- 
trations have  the  same  general  form  as  for  salts  of  simpler  type,  and  that 
they  vary  in  a  similar  manner  as  the  nature  of  the  solvent  varies.  In 
the  following  tables  are  given  values  for  the  conductances  of  Cu(N03)2 
and  K2Hg(CN)4  in  ammonia.27 

TABLE  XXXVIII. 
CONDUCTANCE  OF  TERNARY  SALTS  IN  NH3  AT  — 33°. 

Cu(N03)2  K2Hg(CN)4 

FA  FA 

1.5                  98.3  2.0                198.8 

4.9                  82.9  5.0                182.7 

9.9                  78.2  19.6                159.8 

19.9                  80.9  49.8                169.2 

323.0                151.8  590.0                298.9 

1300.0                213.7  4545.0                493.1 
11190.0                417.0 
22450.0                498.0 

It  will  be  observed  that,  in  both  cases,  the  conductance  passes  through 
a  minimum  value  at  concentrations  in  the  neighborhood  of  0.1  normal. 
In  other  words,  an  increase  in  the  conductance  with  the  concentration  at 
the  higher  concentrations  is  not  confined  to  binary  electrolytes,  but  is 
more  or  less  typical  of  all  electrolytes.  It  appears,  therefore,  that  the 
general  form  of  the  conductance  function  is  the  same  for  electrolytes  of 
different  types.  What  the  precise  form  of  the  equation  may  be,  however, 
has  not  been  determined,  since  the  A0  values  are  unknown  and  the  prob- 
lem is  complicated  owing  to  the  possible  formation  of  intermediate  ions. 

*  Franklin,  Ztschr.  f.  phys.  Chem.  69,  272   (1909). 


Chapter  V. 

The  Conductance  of  Solutions  as  a  Function  of 
Their  Viscosities. 

1.  Relation  Between  the  Limiting  Conductance  A0  and  the  Viscosity 
of  the  Solvent.  One  of  the  factors  upon  which  the  conductance  of  a 
solution  depends  is  the  viscosity  of  the  solution  itself.  If  conductance 
is  due  to  the  motion  of  charged  particles  through  a  medium,  then  the 
speed  of  the  particles  will  obviously  depend  upon  the  resistance  which 
the  particles  experience  in  their  motion;  that  is,  upon  the  viscosity  of 
the  medium.  Unless  the  solutions  are  concentrated,  their  viscosities  will 
not  differ  materially  from  that  of  the  pure  solvent.  We  should  therefore 
expect  that  the  viscosity  of  the  pure  solvent  would  determine  the  motion 
of  particles  under  otherwise  given  conditions.  We  shall  accordingly 
examine  the  relation  between  the  conductance  and  the  viscosity  of  solu- 
tions in  different  solvents.  In  very  dilute  solutions  we  may  expect  that 
the  motion  of  a  given  particle  will  be  practically  independent  of  that  of 
other  particles  of  the  electrolyte  which  may  be  present  in  the  solution.  In 
the  limit,  therefore,  the  A0  values  will  be  determined  by  the  nature  of  the 
moving  particles  and  by  that  of  the  solvent  medium  in  which  they  move. 
In  Table  XXXIX  1  are  given  fluidity  and  A0  values  for  solutions  in  a 
number  of  solvents,  together  with  the  values  of  the  ratio  A0/F. 

TABLE  XXXIX. 
FLUIDITY  AND  A0  VALUES  FOR  ELECTROLYTES  IN  DIFFERENT  SOLVENTS. 


Solvent 

Water 

Ammonia 

Sulphur  dioxide 
Benzonitrile    . 


Temp. 

18° 

—33° 

—10° 

25° 

Epichlorohydrin  25° 

Propylalcohol 18° 

Acetone  18° 

Methylethylketone  25° 

Pyridine 18° 

Isobutylalcohol  25° 

Acetoaceticester  18° 

Isoamylalcohol  25° 

Ethylenechloride  25° 

1  These  values  are  taken  from  Kraus  and  Bray  (Zoo.  cit.,  p.  1383),  excepting  those  for 
water  and  the  viscosity  data  for  sulphur  dioxide  for  which  see  Fitzgerald,  J.  Phya.  Chem. 
16,  621  (1912). 

109 


?  =  l/< 

P      A0 

\0/F  Electrolyte 

93.9 

111.0 

1.173          Nal 

391.0 

301.2 

0.770             " 

233.4 

199.0 

0.854            KI 

80.0 

49.0 

0.613           Nal 

97.1 

62.1 

0.649     (C2H5)<NI 

42.5 

20.6 

0.486           Nal 

304.0 

167.0 

0.550 

249.0 

139.0 

0.560             " 

101.0 

61.0 

0.603             " 

29.6 

13.7 

0.463              " 

59.4 

30.7 

0.517             " 

27.2 

9.2 

0.338             " 

127.9 

66.7 

0.522      (C3H7)4NI 

110        PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

So  far  as  possible  the  same  electrolyte,  namely  sodium  iodide,  has  been 
employed  for-  the  purpose  of  comparison.  In  a  few  cases,  however, 
results  with  this  electrolyte  are  not  available  and  the  data  for  other 
iodides  are  therefore  given.  If  the  speed  of  the  ions  is  solely  a  function 
of  the  viscosity  of  the  solvent  and  is  independent  of  the  nature  of  the 
electrolyte,  the  nature  of  the  solute  will  have  no  influence  on  the  ratio  of 
conductance  to  fluidity.  As  we  shall  see  below,  this  is  not  the  case.2 
On  examining  the  table  it  will  be  seen  that  the  limiting  value  of  the 
conductance  is  roughly  proportional  to  the  fluidity  of  the  solvent.  The 
ratios  A0/F  given  in  the  last  column  vary  between  0.338  for  isoamyl- 
alcohol  and  1.173  for  water.  These  are,  however,  extreme  values,  and  in 
the  greater  number  of  cases  the  ratio  has  a  value  of  approximately  0.6. 
The  three  inorganic  solvents,  water,  ammonia  and  sulphur  dioxide,  show 
exceptionally  high  values  of  the  conductance-fluidity  ratio.  The 
higher  alcohols  have  exceptionally  low  values,  the  value  in  general 
being  the  smaller  the  more  complex  the  alcohol.  In  comparing 
the  A0  values  of  the  salts  in  different  solvents,  we  are  comparing  the 
sum  of  the  conductances  of  the  two  ions.  We  may  therefore  expect 
to  obtain  a  more  nearly  comparable  result  if  we  compare  the  con- 
ductances, not  of  the  electrolytes,  but  of  the  individual  ions  of  the  elec- 
trolytes. The  ratios  of  the  ionic  conductances  for  the  different  ions  in 
ammonia  and  in  water  have  been  given  in  Table  V.  An  examination  of 
that  table  shows  that  the  ratios  of  the  ionic  conductances  vary  all  the 
way  from  2.03  to  3.36,  while  the  ratio  of  the  fluidities  of  the  two  solvents 
is  4.15.  It  follows,  therefore,  that  the  ratio  of  the  A0  values  for  a  given 
electrolyte  in  different  solvents  cannot  be  a  constant,  since  the  ratios  of 
the  ion  conductances  vary  for  different  ions. 

If  a  comparison  is  to  be  made  between  the  conductance  and  the 
fluidity  of  electrolytes  in  different  solvents,  it  might  be  expected  that 
more  nearly  comparable  results  would  be  obtained  if  the  more  slowly 
moving  ions  were  chosen  for  the  purpose  of  comparison.  For  example, 
in  water  at  18°,  the  ratio  of  the  conductance  of  the  acetate  ion  to  the 
fluidity  of  water  is  0.367,3  while  in  ammonia  the  ratio  of  the  conductance 
of  the  CH3CONH~  ion  to  the  fluidity  of  ammonia  at  its  boiling  point 
is  0.330. 

Apparently,  therefore,  the  ratio  of  the  ionic  conductance  to  the 
fluidity  of  the  solvent  approaches  a  constant  limiting  value  somewhere 

•Walden  [ZtacTir.  f.  phya.  Chem.  78,  257  (1912)]  believes  to  have  shown  that,  with  a 
few  exceptions,  the  ratio  \0/F  is  constant.  In  this  he  has  been  misled  as  a  result  of 
employing  A0  values  obtained  by  extrapolating  with  the  cube  root  formula  of  Kohlrausch 
which  is  not  applicable. 

a  Based  on  the  value  34.6  for  the  conductance  pf  the  acetate  ion.  Johnston.  J.  Am 
Chem.  SQC.  31,  10JO  (1909), 


THE  CONDUCTANCE  OF  SOLUTIONS— VISCOSITIES  111 

in  the  neighborhood  of  0.3  as  the  ions  become  more  complex;  that  is, 
as  the  speed  of  the  ions  decreases.  It  follows  that,  in  the  case  of  very 
slowly  moving  ions,  the  speed  is  inversely  proportional  to  the  viscosity 
of  the  medium,  more  or  less  independent  of  the  nature  of  the  solvent 
itself.  It  is  interesting  to  compare  the  speed  of  ions  due  to  radiations 
with  the  speed  of  ordinary  ions  in  different  solvents.  In  Table  XL  * 
are  compared  the  speeds  of  the  acetate  ion  in  water,  the  lithium  ion  in 
ammonia,  and  the  positive  and  negative  ions  in  hexane.  In  the  last 
column  are  given  the  values  of  the  ratio  of  the  speed  of  the  ions  to  the 
fluidity  in  arbitrary  units. 

TABLE  XL. 
COMPARISON  OF  IONIC  SPEEDS  IN  DIFFERENT  SOLVENTS. 

Speed  of  ion 
Solvent          Ion  S  X  10*  F  S/F 

Water  Acetate  3.58  95.35  3.76 

Ammonia  Lithium  11.60  390.8  2.97 

Hexane  Positive  6.03  312.0  1.98 

Hexane  Negative  4.17  312.0  1.34 

It  will  be  observed  that  both  positive  and  negative  ions  in  hexane  move 
decidedly  slower  than  even  the  slowest  moving  ion  in  ammonia  or  in 
water,  taking  into  account  the  relative  viscosities  of  the  solvent  media. 
Apparently,  in  solvents  of  very  low  dielectric  constant,  the  speed  of  the 
ions  relative  to  the  fluidity  of  the  solvent  is  smaller  than  it  is  in  solvents 
of  higher  dielectric  constant.  It  may  be  inferred,  therefore,  that  the 
positive  and  negative  carriers  in  hexane  are  associated  with  a  con- 
siderable number  of  the  solvent  molecules,  as  a  result  of  which  their 
speed  is  relatively  low  with  respect  to  that  of  the  ordinary  ions  in  water 
and  ammonia. 

2.  Change  of  Conductance  as  Result  of  Viscosity  Change  Due  to  the 
Electrolyte  Itself.  At  higher  concentrations  the  viscosity  is  a  function 
of  the  concentration  of  the  solution,  and,  in  most  cases,  increases  with 
it.  In  aqueous  solutions  there  are,  however,  many  eases  in  which  the 
viscosity  decreases  at  higher  concentrations,  or  rather,  in  which  the  vis- 
cosity passes  through  a  minimum,  beyond  which  it  again  increases  as  the 
concentration  increases.  The  viscosity  effect  of  the  electrolyte,  there- 
fore, is  a  property  depending  on  the  electrolyte  as  well  as  on  the  solvent. 
Solutions  which  exhibit  a  negative  viscosity  change  with  the  concentra- 
tion, that  is,  whose  viscosity  decreases  with  increasing  concentration  are 

4£raus;  J.  Am.  Chem.  Spc.  36,  35   (1914), 


112        PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

also  found  in  glycerine.  In  general,  however,  the  negative  viscosity 
effect  appears  only  in  the  case  of  solutions  in  solvents  having  high  dielec- 
tric constants.  As  a  rule,  only  those  salts  which  show  relatively  a  slight 
tendency  to  form  stable  hydrates  exhibit  a  negative  viscosity  effect  in 
solution.  In  Table  XLI  are  given  examples  of  the  relative  viscosities  of 
solutions  in  ammonia,5  water,  and  methylamine5  at  a  number  of  con- 
centrations. 

TABLE  XLI. 

COMPARISON  OF  THE  VISCOSITY  CHANGE  DUE  TO  ELECTROLYTES  IN 
DIFFERENT  SOLVENTS. 

Solvent  Solute     Relative  Viscosity  at  Concentration: 

0.5  1.0  2.5 

Water LiCl  1.05  1.10  1.42 

Ammonia KI  1.16  1.38  2.38 

Methylamine  ....  AgN03  1.40  1.96  6.38 

It  will  be  observed  that  in  a  0.5  normal  solution  the  viscosity  increase 
for  potassium  iodide  in  ammonia  is  approximately  three  times  that  of 
lithium  chloride  dissolved  in  water,  while  the  viscosity  change  for  silver 
nitrate  in  methylamine  at  the  same  concentration  is  approximately  three 
times  that  of  potassium  iodide  in  ammonia.  Approximately  the  same 
ratio  of  increase  holds  at  somewhat  higher  concentrations.  In  this  con- 
nection it  should  be  noted  that  the  viscosity  effect  in  the  case  of  lithium 
chloride  is  relatively  very  great  compared  with  that  of  other  salts  in 
water.  In  the  case  of  potassium  iodide  the  viscosity  effect  is  actually 
negative  in  water.  We  see,  therefore,  that  the  lower  the  dielectric  con- 
stant of  the  solvent,  the  greater  is  the  increase  in  viscosity  due  to  the 
added  electrolyte.  The  dielectric  constants  are  approximately  80,  22 
and  10  for  water,  ammonia,  and  methylamine  respectively.  There  are 
no  data  available  relative  to  the  viscosity  of  solutions  in  the  higher 
amines,  but  qualitative  data  indicate  that  the  viscosity  effect  increases 
very  greatly  with  increasing  complexity  of  the  solvent,  or,  rather,  with 
decreasing  dielectric  constant  of  the  solvent.  It  is  evident  that  there  is 
a  relation  between  the  magnitude  of  the  viscosity  effect  due  to  an  elec- 
trolyte and  the  dielectric  constant  of  the  solvent  in  which  this  electrolyte 
is  dissolved. 

In    Figure    16    are    shown    curves6    representing   the    relation    be- 
tween  the   viscosity    and   the    concentration   of    aqueous    solutions    of 

8  Fitzgerald,  loc.  cit. 

•Sprung,  Pogg.  Ann.  d.  Phys.  159,  1  (1876). 


THE  CONDUCTANCE  OF  SOLUTIONS— VISCOSITIES 


113 


potassium  iodide  at  0°,  30°,  and  60°  and  sodium  chloride  at  10°,  30°,  and 
60°.  It  will  be  observed  that  the  viscosity  in  the  case  of  potassium 
iodide  at  0°  passes  through  a  minimum  in  the  neighborhood  of  2%  nor- 
mal, after  which  it  again  increases.  At  higher  temperatures  the  minimum 
is  displaced  toward  lower  concentrations  and  finally  disappears.  The 
negative  viscosity  effect  decreases  rapidly  with  increasing  temperature 
and  in  most  cases  disappears  in  the  neighborhood  of  30°.  At  still  higher 
temperatures  the  viscosity  effect  becomes  positive.  In  general,  the  posi- 
tive viscosity  effect  increases  markedly  with  the  temperature.  • 


2.2 
2.0 
1,6 

.   1-6 

o 

X    J.4 

I    Ii2 

> 

1.0 

0.8 
0.6 


o.o 


1.0 


4.0 


S.O 


2,O  3.0 

Concentration. 

FIG.  16.    Viscosity  of  Aqueous  Solutions  at  Different  Concentrations. 

In  glycerine  solutions,7  ammonium  iodide,  potassium  iodide,  and 
rubidium  iodide  exhibit  negative  viscosity  effects.  Lithium  chloride,  on 
the  other  hand,  as  in  water,  exhibits  a  viscosity  increase  withc  increasing 
concentration.  In  glycerine  solutions,  the  negative  viscosity  effect  dis- 
appears in  the  neighborhood  of  75°. 

It  is  obvious  that,  if  the  viscosity  of  a  solution  changes  with  concen- 
tration, the  speed  of  the  carriers,  to  which  the  conductance  of  the  solu- 
tions is  due,  will  likewise  change  with  the  concentration.  If  this  is  the 

case,  then  the  conductance  ratio,  y  =  -r-,  no  longer  measures  correctly 

AQ 

'Davis  and  Jones,  Ztachr.  }.  phys.  Chem.  81,  68  (1913). 


114        PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

the  degree  of  ionization.  It  has  been  proposed  to  take  account  of  the 
change  of  conductance  due  to  the  viscosity  effect  in  direct  proportion  to 
the  fluidity  change  of  the  solution.8  In  that  case  the  degree  of  ionization 
of  the  electrolyte  is  given  by  the  expression: 

/Af\\  &     FO 

(40)  Y  =  2C7' 

where  Fa  is  the  fluidity  of  the  pure  solvent  and  F  that  of  the  solution. 
Other  writers  *  have  proposed  an  equation  of  the  form: 


(41)  Y  =  ^ 

where  p  is  a  constant,  and  A  and  A0  are  ionic  conductances.  If  p  were 
equal  to  unity,  the  conductance  of  the  solution  would  be  corrected  in 
direct  proportion  to  the  fluidity  change.  Difficulty  arises  in  determining 
the  value  of  p.  It  has  been  suggested  that  the  value  of  this  constant 
may  be  derived  from  the  manner  in  which  the  speed  of  an  ion  in  dilute 
solution  changes  as  a  function  of  the  temperature.  As  we  shall  see 
presently,  the  change  in  the  A0  values  of  the  ions  is  not  in  general 
directly  proportional  to  the  fluidity  change  of  the  solvent,  but  is  in  most 
cases  smaller.  It  has  been  shown  that  a  relation  of  the  type 

(42)  A  =  KFP 

holds  very  nearly.10  The  values  of  the  constant  p  for  different  salts  are 
given  in  Table  XLII. 

TABLE  XLII. 

VALUE  OF  THE  VISCOSITY-TEMPERATURE  EXPONENT  p  FOR 
DIFFERENT  IONS. 

Univalent  Ions. 

Ion  Cl-         K+       NH4+      N03-  Ag+  Na+  CH3COO 

p   88          .887        .891        .807  .949  .97          1.008 

A 65.4        64.7        64.4        61.8  54.  43.5        34.6 

Divalent  Ions. 

Ion  1/2S04~      1/2  C  A"  1/2  Ba"  1/2  Ca" 

p 0.944  .931  .986  1.008 

A 68.7  63.8  55.9  52.1 

)usfleld  and  Lowry,  Phil.  Trans.   [A]   20k,  289    (1903)  ;  Noyes  and  Falk,  J.  Am. 

•Washburn,  J.  Am.  Chem.  8oc.  S3,  1463  (1911). 
"Johnston,  J.  Am.  Chem.  Soc.  SI.  1010  (1909). 


THE  CONDUCTANCE  OF  SOLUTIONS—  VISCOSITIES  115 

Since  p  is  in  general  less  than  unity,  it  follows  that  the  conductance  of 
the  ions  changes  less  rapidly  than  does  the  viscosity  of  the  solvent  for  a 
given  increase  in  temperature.  As  a  rule,  the  lower  the  conductance  of 
the  ion,  the  greater  the  value  of  the  exponent  p.  For  most  slowly  mov- 
ing ions  the  exponent  appears  to  approach  the  value  unity  as  a  limit. 
This  is  exemplified  in  the  case  of  the  acetate  and  the  calcium  ions.  The 
lower  the  conductance  of  an  ion,  therefore,  the  more  nearly  does  the 
conductance  change  in  direct  proportion  to  the  fluidity  change  of  the 
solvent.  But  while  the  value  of  p  in  Equation  42  h^s  thus  been  evalu- 
ated, there  is  no  good  reason  for  believing  that  the  exponent  p  in  Equa- 
tion 41  will  have  the  same  value.  It  obviously  is  not  possible  to  deter- 
mine the  manner  in  which  correction  should  be  applied  for  the  change 
in  the  conductance  of  solutions  due  to  concentration  change,  unless  we 
know  the  manner  in  which  the  ionization  at  these  concentrations  varies 
as  a  function  of  concentration.  In  other  words,  the  nature  of  the  cor- 
rection as  found  will  depend  upon  the  assumed  nature  of  the  conductance 
function. 

We  have  the  equation: 


where  /(C)  is  some  function  of  the  concentration  of  the  solution.  As  we 
have  seen,  in  solutions  at  higher  concentrations,  the  function  K'  follows 
approximately  the  relation: 


where  n  has  a  value  in  the  neighborhood  of  1.5  for  aqueous  solutions. 
Assuming  this  equation  to  hold  at  higher  concentrations,  we  may  deter- 
mine the  nature  of  the  viscosity  correction  on  the  basis  of  this  assump- 
tion. In  order  to  determine  the  nature  of  the  correction,  therefore,  we 
may  determine  the  value  of  the  constants  n  and  D  at  lower  concentra- 
tions, where  the  viscosity  change  is  negligible,  and  thereafter  extrapolate 
this  function  to  higher  concentrations.  In  other  words,  by  means  of 
Equation  9a  we  may  calculate  the  value  of  y  at  higher  concentrations 
and  compare  it  with  the  directly  measured  value  and  with  the  fluidity 
of  the  solution  at  that  concentration.  Or,  conversely,  the  experimentally 
determined  conductance  values  at  higher  concentrations  may  be  multi- 
plied by  an  assumed  correction  factor  and  the  corrected  values  compared 
with  the  values  calculated  by  means  of  the  above  equation.  If  the 
assumptions  made  are  applicable,  then  the  two  values  should  correspond. 


116        PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 


The  simplest  correction  would  be  that  in  which  the  conductances  were 
assumed  to  change  in  direct  proportion  to  the  fluidity  change  of  the 
solution. 

This  method  of  correction  has  been  applied  to  solutions  of  potassium 
iodide  dissolved  in  water  at  O0.11  In  Figure  17,  lower  curve,  are  plotted 
values  of  log'(CA)  and  of  log[C(A0  —  A)],  both  for  the  measured  (rep- 


0.5 


Log  (cA)  for  LiCl. 

I.O 


1-5 


s 


I  " 
3 

iS   0.0 

5 

T.o 

2.0 


3.0 


X* 


o 


I 

4 

$ 


T.o 


Log  (cA)  for  KI. 


3.0 


FIG.  17.    Showing  Influence  of  Viscosity  Correction  on  the  Conductance  Curves  of 
KI  and  LiCl  in  Water  at  0°. 

resented  by  crosses)  and  the  corrected  (represented  by  circles)  con- 
ductance values  of  potassium  iodide  dissolved  in  water  at  0°.  If  Equa- 
tion 9a  holds  and  if  the  assumed  viscosity  correction  is  applicable,  then 
the  corrected  points  should  lie  upon  a  straight  line.12  This,  apparently, 
is  the  case. 

The  conductance  curve  of  potassium  iodide  in  water  at  0°  is  a  very 
exceptional  one  in  that  at  higher  concentrations  it  passes  through  a  slight 
minimum  and  maximum,  after  which  the  conductance  decreases  very 
rapidly  with  increasing  concentration.  This  form  of  the  curve  is  due 


11  Kraus,  J.  Am.  Chem.  Soc.  36,  35   (1914). 

12  Equation  9a  may  be  written  :  n  log  (CA)  =  log  [C7(Ao 


A)  ]  +  log  ZM< 


THE  CONDUCTANCE  OF  SOLUTIONS-VISCOSITIES 


117 


to  the  viscosity  change  of  the  solution  at  higher  concentrations.  As  we 
have  seen,  the  fluidity  passes  through  a  maximum,  after  which  it  de- 
creases sharply.  If  the  values  of  the  conductance  as  calculated  from 

jji 

Equation  9a  are  multiplied  by  the  fluidity  ratio  •=-,  then  these  calculated 
values  fall  upon  a  curve  (B)  exhibiting  a  slight  maximum  and  minimum, 


g   60 


a 

r 
i 


\  \ 


1.30 


Log  (Concentration). 

FIG.  18.    Showing  the  Influence  of  Fluidity  Change  on  the  Conductance  Curve  of 

KI  in  Water  at  0°. 

which  practically  coincides  with  the  curve  of  measured  conductances,  as 
may  be  seen  from  Figure  18.  It  is  apparent  that  in  the  case  of  solu- 
tions of  potassium  iodide  in  water — and,  in  fact,  this  has  been  shown 
to  be  true  for  aqueous  solutions  of  all  electrolytes  exhibiting  a  negative 
viscosity  effect — the  speed  of  the  ions  changes  in  direct  proportion  to  the 
fluidity  change  of  the  solution.  The  peculiar  form  of  the  conductance 
curve,  as  we  have  it  in  solutions  of  the  potassium  iodide,  is  due  to  the 
variation  of  the  viscosity  effect. 


118        PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

In  solutions  of  electrolytes  in  water  which  exhibit  a  positive  viscosity 
effect,  the  conductance  appears  to  change  less  than  the  viscosity  of  the 
solution.  If  we  treat  the  conductance  curve  of  lithium  chloride  in  a 
manner  similar  to  that  employed  in  the  case  of  potassium  iodide,  we 
obtain  as  plot  not  a  straight  line,  but  a  curve  lying  below  the  straight 
line  resulting  from  Equation  9a.  In  other  words,  the  conductance  values 
appear  to  be  overcorrected.  This  result  is  illustrated  in  Figure  17,  upper 
curve,  in  which  A  is  the  uncorrected  curve,  B  is  the  curve  in  which  the 
conductance  is  corrected  in  direct  proportion  to  the  fluidity  change, 
while  C  is  a  curve  in  which  correction  has  been  applied  to  the  lithium 
ion  only.  We  may  conclude,  therefore,  that,  in  aqueous  solutions,  the 
conductance  may  be  corrected  for  the  viscosity  change  in  direct  propor- 
tion to  the  fluidity  change  in  the  case  of  salts  which  exhibit  a  negative 
viscosity  effect,  but  that,  in  solutions  of  salts  which  exhibit  a  positive 
viscosity  effect,  the  correction  made  should  be  smaller.  Just  what  cor- 
rections should  be  applied  is  difficult  to  determine  at  the  present  time. 

We  have  seen  that  in  non-aqueous  solutions  the  viscosity  effect  is 
much  larger  than  it  is  in  aqueous  solutions.  We  should  therefore  expect 
that  the  conductance  of  non-aqueous  solutions  would  be  affected  to  a 
much  greater  extent  than  that  of  aqueous  solutions.  It  appears,  how- 
ever, that  in  solutions  of  electrolytes  in  non-aqueous  solvents  the  con- 
ductance changes  much  less  than  the  fluidity  of  the  solvent. 

The  relation  between  the  conductance  and  the  viscosity  is  illustrated 
in  Figure  19,  in  which  are  plotted  the  conductance  and  fluidity  values 
of  solutions  of  potassium  iodide  in  liquid  ammonia  at  different  concen- 
trations. Branch  B  is  extrapolated  on  the  assumption  that  Equation  9a 
holds.  There  is  also  indicated  on  this  figure  the  calculated  conductance 
of  these  solutions,  Branch  D,  on  the  assumption  that  the  conductance 
changes  in  direct  proportion  to  the  fluidity  of  the  solvent.  It  will  be 
observed  that  the  conductance,  as  corrected  in  this  way,  is  much  too  low 
to  correspond  with  the  experimental  conductance  curve  represented  by 
circles.  It  is  evident,  therefore,  that  in  non-aqueous  solutions  the  con- 
ductance change  is  smaller  than  corresponds  to  the  viscosity  change. 
This  is  further  borne  out  by  the  fact  that  Equation  11  appears  to  hold 
for  solutions  of  many  electrolytes  up  to  concentrations  at  times  as  high 
as  2  normal.  It  is  obvious  that  the  viscosity  of  the  solutions  at  these 
concentrations  must  be  much  greater  than  that  of  the  pure  solvent,  and 
consequently  it  follows  that  the  correction  to  be  applied  for  the  viscosity 
change  is  probably  the  smaller  the  greater  the  viscosity  change;  that  is, 
the  lower  the  dielectric  constant  of  the  solvent.  On  the  other  hand,  it 
has  been  found,  in  the  case  of  all  solutions  in  non-aqueous  solvents,  that, 


THE  CONDUCTANCE  OF  SOLUTIONS— VISCOSITIES 


119 


at  sufficiently  high  concentrations,  the  conductance  curve  ultimately  falls, 
and  falls  the  more  rapidly  the  higher  the  concentration.  There  appears 
to  be  no  exception  to  this  behavior.  There  can  be  little  question  but 
that  the  final  decrease  in  the  conductance  is  due  to  a  large  increase  in  the 
viscosity  of  the  medium.  This  is  illustrated  in  Figure  20,  where  the 
conductance  of  solutions  of  silver  nitrate  in  methylamine 13  is  repre- 
sented as  a  function  of  the  concentration.  The  maximum  lies  a  little 


19* 


160 


128 


•§ 

1" 


0.96 


'— 
£ 


- 


i.i 


0.8 


I/>K  (concentration). 


FIG.  19.    Showing  the  Influence  of  Fluidity  Change  on  the  Conductance  of  Solutions 

of  KI  inNHaat—  33.5°. 

above  normal  concentration  at  — 33°  and  is  displaced  toward  higher 
concentrations  at  higher  temperatures. 

3.  Relation  between  Viscosity  and  Conductance  on  the  Addition  of 
Non-Electrolytes.  The  addition  of  a  non-electrolyte  to  a  solution  of  an 
electrolyte  in  most  cases  increases  the  viscosity  of  the  solution.1*  The 
conductance  change  on  the  addition  of  a  non-electrolyte  is  in  the  same 
direction  as  that  of  the  viscosity  change,  but  in  most  cases  the  con- 
ductance change  is  smaller  than  the  corresponding  viscosity  change. 

»  Fitzgerald,  Joe.  cit.,  p.  640. 

14  In  a  few  instances,  however,  where  the  added  non-electrolyte  forma  a  stable  complex 
with  one  of  the  ions  in  solution,  the  addition  of  a  non-electrolyte  results  in  a  viscosity 
decrease.  An  example  of  this  effect  is  found  in  solutions  of  certain  of  the  heavy  metals 
in  water  whose  viscosity  is  reduced  on  the  addition  of  ammonia.  [Blanchard,  J.  Am. 
Chem.  Soc.  26,  1315  (1904).]  In  these  cases  the  addition  of  a  non-electrolyte  causes  a 
decrease  in  the  viscosity  only  so  long  as  it  combines  with  the  electrolyte  to  form  the 
complex.  Beyond  this  point  the  viscosity  in  general  increases  with  further  addition  of 
non-electrolyte. 


120        PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 


The  experimental  material  available  is  very  incomplete.  So  far  as  any 
conclusion  may  be  drawn,  however,  the  conductance  change  is  the  more 
nearly  proportional  to  the  fluidity  change,  the  smaller  the  molecules  of 


4S 


40 


1* 


10 


0123 

Log  V. 
FIG.  20.    Conductance  of  Silver  Nitrate  in  Methylamine  at  Different  Temperatures. 

the  added  non-electrolyte.  It  has  been  found  that  the  relation  between 
the  conductance  and  the  viscosity  on  the  addition  of  a  non-electrolyte 
may  be  expressed  by  an  exponential  equation  of  the  form  A0  =  KF^, 
where  A0  is  the  limiting  conductance  of  the  electrolyte  in  solutions  con- 


THE  CONDUCTANCE  OF  SOLUTIONS-VISCOSITIES  121 

taining  the  non-electrolyte  and  F  is  the  fluidity  of  the  solution.  The 
smaller  the  conductance  change  of  the  electrolyte  for  a  given  fluidity 
change,  the  smaller  is  the  value  of  the  exponent  p. 

In  Table  XLIII  are  given  values  of  the  exponent  p  for  aqueous 
solutions  of  a  number  of  electrolytes  in  the  presence  of  non-electrolytes. 

TABLE   XLIII. 

CHANGE  OF  CONDUCTANCE  OF  ELECTROLYTES  DUE  TO  ADDED 
NON-ELECTROLYTES. 

Non-  Raf-      Gly-        Ace-  Methyl 

Electrolyte  Sucrosef    finose*     cerolf     tone$    Ureaf  Alcohol* 

Mol.  Wt 342.1        594.4        92  58  60  32 

p  for  KC1 0.66          0.675        0.83        0.93        0.95        1.2 

t   20°  25°          20°         25°         25°         25° 

Methyl    Methyl 
Non-Electrolyte          Sucrosef   Raffinose*    Raffinose*  Alcohol*  Alcohol* 

Electrolyte  HC1  CsCl  LiCl  CsCl        LiCl 

p    0.55  0.676  0.669  0.8  1.1 

°*°  25°  25°  25°  25° 


Non-Electrolyte 

AcetoneJ 

Glycerol§ 

Urea§ 

Pyridine§ 

Electrolyte 

HC1 

CuS04 

NaOH 

LiN03 

v    . 

1.0 

1.0 

1.0 

1.0-1.3 

t  . 

.  25° 

15° 

25° 

*  Clark,  Thesis,  Univ.  of  111.  (1915).  See  also,  Washburn,  "Principles  of  Physical 
Chemistry,"  2  Ed.,  p.  260. 

t  5holm,  Finskct  Vetenslcap.  Soc.  Forhandl.  55,  A  No.  5,  p.  75  (1913)  ;  Washburn, 
loc.  cit. 

t  Ryerson,  Thesis,  Univ.  of  111.  (1915). 

§  Green,  J.  Chem.  Soc,  93,  2049   (1908). 

It  will  be  seen  from  the  table  that,  in  general,  the  higher  the  molecu- 
lar weight  of  the  added  non-electrolyte,  the  smaller  is  the  value  of 
the  exponent  p.  This  is  most  clearly  shown  in  the  case  of  potassium 
chloride,  for  which  electrolyte  the  data  are  more  extensive  than  for 
others.  The  exponent  in  the  presence  of  sucrose  and  raffinose  is  in  the 
neighborhood  of  0.67,  while  in  the  presence  of  urea  it  is  0.95  and  in  the 
presence  of  methyl  alcohol  1.2.  The  molecular  weight  of  the  added  elec- 
trolyte is  thus  a  governing  factor  in  determining  the  manner  in  which 
the  conductance  of  an  ion  varies  due  to  viscosity  change.  That  some 
transpositions  in  the  order  of  the  exponent  and  in  that  of  the  molecular 
weight  of  the  added  non-electrolyte  will  occur  is  to  be  expected,  since 
specific  influences  may  make  themselves  felt.  It  is  noticeable  that  in 
the  case  of  methyl  alcohol  the  exponent  has  a  value  greater  than  unity. 


122        PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

The  significance  of  this  result  remains  uncertain.  It  is  to  be  expected, 
however,  that,  on  the  addition  of  an  electrolyte  whose  molecular  weight 
is  lower  than  the  mean  of  that  of  the  solvent  molecules,  effects  may  occur 
which  cannot  well  be  predicted  on  the  basis  of  our  present  knowledge  of 
the  viscosity  relations  in  such  mixtures.  It  is  interesting  to  note  that, 
in  the  presence  of  non-electrolytes  of  high  molecular  weight,  the  coeffi- 
cient for  different  electrolytes  has  very  nearly  the  same  value.  Thus, 
in  the  presence  of  raffinose  the  values  of  the  exponent  for  lithium,  potas- 
sium and  caesium  chlorides  are  very  nearly  identical.  Since  these  salts 
have  a  common  anion,  it  may  be  inferred  that  the  influence  of  the  vis- 
cosity effect  due  to  non-electrolytes  of  high  molecular  weight  is  the  same 
for  the  lithium,  potassium  and  caesium  ions.  This  is  apparently  not  so 
nearly  true  in  the  presence  of  non-electrolytes  of  low  molecular  weight, 
but  even  here,  in  some  instances  at  any  rate,  the  exponent  does  not  differ 
greatly  for  different  salts.  It  would  seem  that  the  influence  of  the  vis- 
cosity change  on  the  .conductance  of  an  ion,  due  to  the  electrolyte  itself, 
differs  markedly  from  that  due  to  the  addition  of  a  non-electrolyte.  At 
the  present  time,  sufficient  data  are  not  available  to  enable  us  to  draw 
conclusions  with  any  considerable  degree  of  certainty. 

4.  The  Influence  of  Temperature  on  the  Conductance  of  the  Ions. 
As  is  shown  in  Table  XLII,  with  increasing  temperature  the  conductance 
of  the  ions  increases,  and  this  increase  is  the  more  nearly  proportional 
to  the  increase  in  the  fluidity  of  the  solvent,  the  lower  the  conducting 
power  of  the  ion.  In  the  case  of  the  acetate  ion,  the  conductance  is 
everywhere  proportional  to  the  fluidity  of  water  from  0°  to  156°,  which 
is  the  entire  interval  over  which  the  viscosity  of  the  solvent  has  been 
measured.  In  the  following  table  are  given  the  ratios  of  the  fluidity  of 
water  to  the  conductance  of  the  acetate  ion  from  0°  to  156°. 15 

TABLE   XLIV. 

RATIO  OP  THE  FLUIDITY  OF  WATER  TO  THE  CONDUCTANCE  OF  THE  ACETATE 
ION  AT  DIFFERENT  TEMPERATURES. 

Temp 0°        18°       25°       50°       75°       100°      128°      156° 

-T ....  2.73      2.72      2.73      2.72      2.71      2.72      2.71       2.71 

ACH3COCT 

It  is  evident  that,  in  dilute  solutions,  the  conductance  of  the  acetate  ion, 
and  presumably  therefore  its  speed,  is  directly  proportional  to  the  fluidity 
of  the  solvent. 

Since  the  conductance  of  the  acetate  ion  is  proportional  to  the  fluidity 

"  Johnston,  loc.  cit. 


THE  CONDUCTANCE  OF  SOLUTIONS— VISCOSITIES  123 

of  water  up  to  156°,  we  may  assume,  in  the  absence  of  experimental 
data,  that  it  remains  proportional  at  higher  temperatures.  In  order, 
therefore,  to  compare  the  conductance  of  the  different  ions  with  the 
fluidity  of  water,  we  may  compare  the  conductance  of  these  ions  with 
that  of  the  acetate  ion  whose  values  are  known  up  to  306°.  The  ratio 
of  the  conductances  of  the  various  ions  to  that  of  the  acetate  ion  is  given 
in  Table  XLV.16 

TABLE   XLV. 

INFLUENCE  OF  TEMPERATURE  ON  THE  CONDUCTANCE  OF  VARIOUS  IONS 
RELATIVE  TO  THAT  OF  THE  ACETATE  ION. 

Ion  Conductance  at  temperatures: — 

0.0°  18°  25°  50°  75°  100°  128°  156°  218°  306° 

K+   1.99  1.87  1.83  1.72  1.66  1.58  1.54  1.50  1.32  1.18 

Na+   1.28  1.26  1.25  1.22  1.20  1.19  1.19  1.18  1.15  1.11 

NH4+    ....  1.98  1.86  1.83  1.72  1.66  1.59  1.55  1.52  1.37  1.30 

Ag+ 1.62  1.57  1.54  1.51  1.49  1.45  1.43  1.42  1.29  .. 

Cl-    2.02  1.89  1.85  1.73  1.67  1.59  1.54  1.51  1.32  1.18 

N03-  1.99  1.78  1.73  1.55  1.46  1.37  1.30  1.25  1.21  .. 

H+   11.82  9.08  8.58  6.95  5.88  4.95  4.23  3.68  2.79  1.82 

OH-   5.17  4.95  4.71  4.24  3.75  3.38  3.07  2.81  2.08  1.62 

In  determining  the  conductance  of  the  various  ions,  it  is  of  course 
necessary  to  assume  values  for  the  transference  numbers  of  one  pair  of 
ions.  In  the  case  of  potassium  chloride,  the  transference  number  is  very 
nearly  0.5  and  at  higher  temperatures  it  appears  to  approach  this  value 
as  a  limit.  It  has  been  assumed,  therefore,  that  at  temperatures  above 
100°  the  transference  number  of  the  potassium  and  chloride  ions  is  0.5. 
This  assumption,  moreover,  is  justified  by  the  fact  that,  as  the  tem- 
perature increases,  the  transference  numbers  of  all  ions  appear  to 
approach  one  another.  In  the  above  table  the  ionic  conductances  at 
the  higher  temperatures  are  based  upon  this  assumption. 

The  relation  between  the  ionic  conductances  and  the  temperature  is 
shown  in  Figure  21,  where  the  conductances  relative  to  the  acetate  ion  are 
plotted  as  ordinates  and  the  temperatures  as  abscissas.  Since  the  con- 
ductance of  the  acetate  ion  is  proportional  to  the  fluidity  of  the  solvent, 
it  follows  that  the  ordinates  will  be  proportional  to  the  ratio  of  the  ionic 
conductances  to  the  fluidity  of  the  solvent.  On  examining  the  figure, 
it  will  be  seen  that  the  greater  the  value  of  the  conductance  of  an  ion, 
the  less  does  the  conductance  increase  as  the  temperature  increases. 

Ai 

That  is,  the  ratio  - —  decreases  with  increasing  temperature  and  de- 

ac 

"Kraus,  loc.  cit. 


124        PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 


creases  the  more,  the  greater  the  value  of  the  ratio.  In  other  words, 
these  ratios  appear  to  approach  unity,  as  a  limit  at  high  temperatures. 
The  conductances  of  all  ions,  therefore,  appear  to  approach  that  of  very 
slowly  moving  ions.  For  example,  at  0°  the  conductance  of  the  hydrogen 
ion  is  11.82  times  that  of  the  acetate  ion,  while  at  306°  it  is  only  1.82 
times  that  of  this  ion.  At  0°  the  conductance  of  the  potassium  ion  is 
1.99  times  that  of  the  acetate  ion,  while  at  306°  it  is  only  1.18  times  that 
of  this  ion.  At  0°  the  conductance  of  the  sodium  ion  is  1.28  times  that 
of  the  acetate  ion,  whereas  at  306°  it  is  only  1.11  times  that  of  the  same 


12 

H+ 


6 
OH- 


t 

Nor 


100°  200' 

Temperature. 


3«> 


d 

FIG.  21.     Showing  the  Relative  Change  of  Ionic  Conductances  with  Temperature. 


ion.  It  is  evident,  therefore,  that  as  the  temperature  increases  the  speeds 
of  the  different  ions  approach  a  common  value.  With  the  exception  of 
the  nitrate  ion,  the  curves  for  the  ionic  conductances  do  not  intersect. 
At  low  temperatures,  however,  the  relative  conductance  of  the  nitrate 
ion,  with  respect  to  that  of  the  acetate  ion,  decreases  much  more  rapidly 
than  it  does  for  other  ions  having  the  same  conducting  power.  At  0° 
the  ratio  of  the  conductance  of  the  nitrate  ion  to  that  of  the  acetate 
ion  is  1.99,  whereas  at  25°  it  is  only  1.73.  In  the  case  of  the  potassium 
ion  at  the  lower  temperature,  the  ratio  is  also  1.99,  but  at  25°  it  is  1.83. 

These  results  have  an  important  bearing  on  our  conceptions  as  to 
the  nature  of  the  conducting  particles,  particularly  as  regards  the  effect 
of  temperature  on  the  speed  of  these  particles.  As  has  been  shown  by 


THE  CONDUCTANCE  OF  SOLUTIONS— VISCOSITIES  125 

means  of  transference  experiments,  the  ions  are  hydrated  in  water.  In 
order  to  account  for  the  fact  that  the  speeds  of  the  different  ions  at 
higher  temperatures  approach  one  another,  it  might  be  assumed  that  the 
hydrates  break  down  at  higher  temperatures,  but  this  assumption  would 
not  be  in  harmony  with  certain  facts.  Since  the  conductance  of  the 
slowly  moving  ions  changes  in  direct  proportion  to  the  fluidity  of  the 
solvent  as  the  temperature  increases,  it  is  reasonable  to  assume  that  the 
relative  dimensions  of  the  ion  complex  remain  practically  constant.  If, 
therefore,  the  speed  of  the  more  rapidly  moving  ions  approaches  that  of 
the  more  slowly  moving  ions  at  higher  temperatures,  it  points  to  a  slow- 
ing up  of  the  more  rapidly  moving  ions  as  the  temperature  increases. 
This  corresponds  to  a  greater  relative  resistance  to  their  motion,  which 
can  only  be  interpreted  as  due  to  an  increase  in  the  dimensions  of  the 
ion-complex.  In  other  words,  as  the  temperature  increases,  the  hydra- 
tion  of  the  more  rapidly  moving  ions  increases,  which  tends  to  reduce 
their  speed  relative  to  that  of  more  slowly  moving  ions. 

If  the  hydration  of  the  ions  is  due  primarily  to  electrical  forces  acting 
between  the  ions,  which  are  charged,  and  the  surrounding  solvent  mole- 
cules, which  have  an  electrical  moment,  then  we  should  expect  that,  as 
the  dielectric  constant  of  the  medium  decreases,  the  size  of  the  complex 
will  increase,  since  in  a  dielectric  medium  the  force  is  inversely  propor- 
tional to  the  dielectric  constant.    For  this  reason  we  should  expect  the 
relative  speeds  of  ions  in  non-aqueous  solvents  of  low  dielectric  constant 
to  approach  one  another  much  more  nearly  than  they  do  in  water.    This 
appears  to  be  the  case.    Moreover,  this  is  also  in  harmony  with  the  fact 
that  in  the  case  of  very  large  ions,  in  other  words,  in  the  case  of  ions 
which  have  a  low  conducting  power,  the  conductance  in  different  sol- 
vents, as  well  as  at  different  temperatures,  is  very  nearly  proportional  to 
the  fluidity  of  the  solvent.    We  may  conclude,  therefore,  that  the  hydra- 
tion of  the  ions  increases,  or,  including  non-aqueous  solvents,  that  the 
solvation  of  the  ions  increases  with  the  temperature  because  of  a  decrease 
in  the  dielectric  constant  of  the  medium.    It  is  not  to  be  assumed,  how- 
ever, that  the  dimensions  of  the  ions  in  different  solvents  are  controlled 
entirely  by  the  dielectric  constant.    The  solvent  may  combine  chemi- 
cally with  a  given  ion  to  form  a  complex,  which  ion  in  turn  may  have 
associated  with  it  additional  solvent  molecules,  due  to  electrical  inter- 
action between  this  ion  and  the  solvent.    We  should  expect  this  to  be 
the  case  with  silver  ions  which  form  an  extremely  stable  complex  with 
ammonia.    Even  in  aqueous  solutions,  the  silver  ion  forms  a  complex 
Ag(NH3)2+  with  ammonia.    This  may  account  for  the  relatively  low 
conducting  power  of  the  silver  ion  in  liquid  ammonia  solution.    Whereas, 


126        PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

for  example,  the  conductance  of  the  lithium  ion  in  ammonia  is  3.36  times 
that  of  the  lithium  ion  in  water,  that  of  the  silver  ion  in  ammonia  is  only 
2.15  times  that  in  water.  So,  also,  we  find  that  the  ammonium  ion  in 
ammonia  has  a  conductance  of  only  2.03  times  that  of  the  ammonium  ion 
in  water,  indicating  the  formation  of  relatively  large  complexes.  In  this 
connection  it  may  be  pointed  out  that  the  ammonium  salts  form  with 
ammonia  saturated  solutions  whose  vapor  pressures  are  extremely  low. 
For  example,  the  vapor  pressure  of  a  saturated  solution  of  ammonium 
nitrate  in  ammonia  is  one  atmosphere  at  26°. 

If  the  complexity  of  the  ions  increases  with  the  temperature,  we 
should  expect  that  at  higher  temperatures  the  viscosity  would  be  in- 
creased more  largely  for  a  given  addition  of  salt  than  at  lower  tem- 
peratures. This,  again,  corresponds  with  observations  on  the  viscosity 
of  solutions.  The  change  of  viscosity  due  to  a  given  addition  of 
salt  increases  as  the  temperature  rises,  and  this  increase  appears  to  be 
the  greater  the  higher  the  temperature.  It  is  to  be  noted,  also,  that  the 
increase  in  viscosity  due  to  the  addition  of  electrolytes  is  much  greater 
than  that  due  to  the  addition  of  non-electrolytes,  except  in  the  case  of 
non-electrolytes  which  have  very  large  molecules.  In  general,  as  has 
already  been  pointed  out,  the  viscosity  effect  is  the  greater  the  lower 
the  dielectric  constant  of  the  solvent.  In  solvents  of  very  low  dielectric 
constant,  the  viscosity  of  some  solutions  becomes  so  great,  at  high  con- 
centrations, that  they  often  become  practically  solid. 

5.  The  Influence  of  Pressure  on  the  Conductance  of  Electrolytic 
Solutions.  As  we  have  seen,  the  conductance  of  the  ions  is  a  function 
of  the  viscosity  of  the  solution.  As  the  hydrostatic  pressure  on  a  solu- 
tion is  increased,  its  viscosity  changes,  the  sign  and  magnitude  of  this 
change  being  dependent  upon  the  nature  of  the  solvent  medium  and 
upon  the  concentration  of  the  solution  in  question.  The  effect  of  pres- 
sure on  the  viscosity  of  solutions  in  water,  as  well  as  the  effect  upon 
water  itself,  has  been  measured  by  Cohen.17  In  Figure  22  are  shown 
the  percentage  changes  of  viscosity  for  pure  water  at  different  pressures 
and  temperatures.  From  an  inspection  of  the  figure  it  will  be  seen 
that  with  increasing  pressure  the  viscosity  of  water  decreases  markedly. 
As  the  temperature  rises,  however,  the  viscosity  effect  diminishes  and 
it  is  evident  that  at  higher  temperatures  the  effect  changes  sign.  From 
the  form  of  the  curves  at  15°  and  23°  it  is  evident  that  at  higher  pres- 
sures the  curves  for  the  viscosity  effect  will  pass  through  a  minimum  and 
that  ultimately,  therefore,  the  viscosity  change  will  change  sign,  the 
viscosity  increasing  with  increasing  pressure.  In  non-aqueous  solvents 

"Cohen.  Wied.  Ann.  J5,  666  (1892). 


THE  CONDUCTANCE  OF  SOLUTIONS— VISCOSITIES  127 

the  viscosity  increases  with  increasing  pressure,  as  was  found  by  Ront- 
gen 18  and  Warburg  and  Sachs  19  for  ether  and  benzene,  and  by  Cohen 
for  turpentine.  In  general,  the  viscosity  effect  in  non-aqueous  solvents 
is  greater  than  that  in  water,  and,  as  we  shall  see  below,  the  effect  is 
the  greater  the  greater  the  viscosity  of  the  medium. 

The  pressure-viscosity  effect  in  solutions  is  a  function  of  the  con- 
Pressure  in  Atmospheres. 
O  ZOO        MOO       000       800       1000 


Fia.  22.    Showing  the  Influence  of  Pressure  on  the  Viscosity  of  Water  at  Different 

Temperatures. 

centration,  as  was  shown  by  Cohen.  In  Figure  23  are  shown  curves 
for  the  viscosity  change  of  solutions  of  sodium  chloride  in  water  at  2° 
and  14.5°.  The  broken  line  curves  relate  to  the  lower  temperature. 
The  concentrations  of  the  various  solutions  are  indicated  on  the  figure. 
With  increasing  concentration  of  the  solution,  the  viscosity  decrease,  due 
to  a  given  increase  in  pressure,  diminishes  and  ultimately  changes  sign; 
that  is,  with  increasing  pressure,  the  viscosity  of  the  solution  increases. 
The  lower  the  temperature,  the  greater  the  influence  of  a  given  pressure 

"Rontgen,  TFied.  Ann.  22,  510   (1884). 

»  Warburg  and  Sachs.  TFied.  Ann.  22,  518  (1884), 


128        PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

change  upon  the  viscosity,  but  at  higher  concentrations  the  effect  of 
temperature  diminishes  greatly. 

Pressure  in  Atmospheres. 


0% 

FIG.  23.    Showing  the  Influence  of  Pressure  on  the  Viscosity  of  Aqueous  Sodium 
Chloride  Solutions  at  Different  Concentrations. 

The  change  in  the  viscosity  of  a  solution  with  pressure  will  obviously 
have  an  influence  upon  the  conductance  of  the  solution.    The  viscosity 


THE  CONDUCTANCE  OF  SOLUTIONS—  VISCOSITIES  129 

effect,  however,  is  not  the  only  one  involved.  As  Tammann  has  shown,20 
the  conductance-pressure  coefficient  is  the  resultant  sum  of  four  effects; 
namely,  the  volume  change  of  the  solution  due  to  pressure  change,  the 
change  in  the  mobility  of  the  ions  due  to  the  viscosity  change  of  the 
solution,  the  change  in  the  ionization  of  the  electrolyte,  and  finally  the 
change  in  the  conductance  of  the  solvent  medium,  which,  as  a  rule,  is  due 
to  a  small  quantity  of  electrolyte  present  as  impurity.  The  conductance- 
pressure  coefficient,  therefore,  is  given  by  the  equation: 


X  Y'  Ap 

where  X  is  the  conductance  of  the  solution  due  to  the  electrolyte,  V  that 
due  to  the  solvent  medium,  y  is  the  ionization  of  the  electrolyte  and  y' 
that  of  the  solvent  medium,  and  cp  is  the  ionic  resistance;  that  is  to  say, 
the  reciprocal  of  the  ionic  mobility.  In  the  equation,  therefore,  the  first 
term  of  the  right-hand  member  measures  the  conductance  change  due 
to  the  volume  decrease  of  the  solution;  the  second  term  measures  the 
conductance  change  due  to  the  viscosity  change  of  the  solution;  the  third, 
the  conductance  change  due  to  the  ionization  change  of  the  electrolyte; 
and  the  last  term,  the  conductance  change  due  to  the  ionization  change 
of  the  solvent  medium.  By  suitably  choosing  the  condition  of  the  solu- 
tion, it  is  possible  to  minimize  the  value  of  various  of  the  terms  enter- 
ing into  this  equation,  and  thus  make  apparent  the  effect  of  the  various 
factors  on  the  conductance  of  the  solution  due  to  pressure  change. 

Let  us  examine  first  the  typical  form  of  the  conductance-pressure 
curves  in  the  case  of  aqueous  solutions  of  0.01  N  KC1.  In  Figure  24  21 
are  represented  values  of  the  ratio  of  the  resistance  of  the  solution,  7?p, 
under  a  pressure  of  p  kilograms  per  square  centimeter  to  the  resistance 
Rp=i  under  a  pressure  of  one  atmosphere  at  a  series  of  temperatures.  It 
will  be  observed  that  as  the  pressure  increases  the  resistance  of  the  solu- 
tion decreases  initially.  As  the  temperature  rises,  the  value  of  the 
decrease  due  to  a  given  pressure  change  diminishes.  At  high  pressures 
the  isotherms  exhibit  a  minimum.  •  The  higher  the  temperature,  the  lower 
the  pressure  at  which  the  minimum  occurs.  It  is  evident  that  at  suffi- 
ciently high  temperatures  the  minimum  will  disappear  and  the  resistance 
of  the  solution  will  increase  throughout  with  increasing  pressure.  This 
has  been  found  to  be  the  case  with  strong  electrolytes,  such  as  sodium 
chloride  in  aqueous  solution. 

In  solutions  of  strong  binary  electrolytes,  the  ionization  at  a  con- 
centration of  0.01  N  is  so  high  that  but  little  change  is  to  be  expected  in 

"  Tammann,  Ztschr.  f.  pTiys.  CJiem.  27,  458   (1898). 
"Korber,  Ztschr.  f.  phys.  Chem.  67,  222   (1909). 


130       PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 


its  value  as  a  result  of  pressure  change.  The  third  term  of  the  right- 
hand  member  of  Equation  43  may  therefore  be  neglected.  The  fourth 
term,  likewise,  may  be  neglected  at  this  concentration,  since  the  con- 
ductance of  the  pure  solvent  is  negligible  in  comparison  with  that  of  the 
solution.  The  observed  conductance  change  of  solutions,  under  these 
conditions,  therefore,  is  due  to  the  first  two  terms.  The  value  of  the  first 

Pressure. 
1000     1500      2000 


1.02 
1.0! 
1.00 

0.99 

0.98 

0.97 


3,095 

^0.94 

0.93 

0.9? 
091 
090 
0.89 

0.88 
057 


500 


3500 


v\ 


\ 


\ 


5000 
99-50* 


78.88° 


59.200 


39.40° 


19.18° 


0.01° 


FIG.  24.    Showing  the  Influence  of  Pressure  on  the  Resistance  of  0.01  N  Aqueous 
KC1  Solutions  at  Different  Temperatures. 

term  of  the  right-hand  member  may  be  calculated  from  the  data  of 
Amagat  on  the  compressibility  of  pure  water,  since  the  compressibility 
of  an  0.01  N  solution  will  not  differ  appreciably  from  that  of  pure  water. 
If  the  first  term  of  the  right-hand  member  is  transposed,  we  have  the 
equation: 


<pAp 


_ 

vAp9 


THE  CONDUCTANCE  OF  SOLUTIONS— VISCOSITIES 


131 


from  which  equation  the  effect  of  pressure  upon  the  conducting  power  of 
the  ions  may  be  determined.  In  a  solution  at  a  concentration  of  0.01  N 
the  effect  of  pressure  on  the  viscosity  will  not  differ  materially  from 
that  on  the  pure  solvent.  It  might  be  expected  that  the  effect  of  pressure 
on  the  conductance  of  the  ions  would  vary  inversely  as  the  viscosity  change 
of  the  solution.  Indeed,  Tammann,  on  comparing  the  conductance-pres- 


Pressure. 

000        ZOOO       ZMO 


tfff 


MOO 


3500 


FIG.  25.    Comparison  of  the  Influence  of  Pressure  on  the  Conductance  and  the 
Fluidity  of  Dilute  Aqueous  NaCl  Solutions  at  Different  Temperatures. 

sure  effects  as  calculated  according  to  Equation  44  for  0.1  N  sodium 
chloride  with  the  measured  viscosity  effects  of  Cohen,  found  almost  an 
exact  correspondence  as  may  be  seen  from  Figure  25.22  The  points  on 
this  figure  represented  by  combined  cross  and  circle  are  measured  vis- 
cosity values  of  Cohen,  while  the  curves  represent  the  values  of  the  vis- 
•cosity  effect  as  determined  from  conductance  measurements  according  to 
Equation  44.  Measurements  by  Korber,23  while  confirming  the  results 
of  Tammann  for  sodium  chloride,  show  that  the  viscosity-conductance 
effect  due  to  pressure  in  the  case  of  different  electrolytes  is  a  function 

"Tammann,  Wted.  Ann.  69,  773  (1899). 

»  Korber,  Ztschr.  f.  phj/s.  Chem.  67,  212  (1909). 


132     PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 


Pressure. 
500    1000    1500    2000   ^500   5 


Cm* 


HCl 


FIG.  26.    Influence  of  Pressure  on  the  Resistance  of  0.01  N  Solutions  of  Different 

Salts  in  Water  at  19.18°. 

of  the  nature  of  the  ions  and  that  the  correspondence  found  for  sodium 
chloride  is  purely  accidental.  # 

In  Figure  26  are  represented  values  of  the  ratio  -5-^-  for  aqueous 


THE  CONDUCTANCE  OF  SOLUTIONS— VISCOSITIES 


133 


4-009 
+  0.08 

+0.07 
+  0.06 
+  0.05 

+  0.03 
+  0.02 
+  0.01 

i^ 

-0.01 
-0.02 
-0.03 
-0.04 
-0.05 
-0.06 
-0.07 
-0.08 

-0/>Q 

Pressure. 
500     1000     1SOO    2000    2500    3000*2 

/ 

Sal 
Kl 

NaBr 
KBr 

Naa 

KCl 

Litl 

H  a 

A 

// 

/ 

/    j 

/ 

// 

// 

/ 

7 

' 

// 

/ 

y 

y 

/  / 

/ 

/  / 

3^ 

;LX 

/, 

y 

// 

/ 

V 

s^ 

^ 

/s 

/ 

^ 

\ 

•  —  - 

/ 

\\ 

\ 

^ 

-~-—~ 

-  —  —  . 

:  —  •  —  i 

\ 

\ 

\ 

v-- 

^__ 

Fia.  27.    Showing  the  Influence  of  Pressure  on 
Aqueous  Solutions  of  Various 


the  Resistance  Coefficients  for 
Electrolytes. 


134       PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 
solutions  of  various  electrolytes  at  a  concentration  of  0.01  N  at  a  tem- 
perature of  19.18°,  while  in  Figure  27  24  are  shown  values  of  -^  as  cal- 
culated from  the  measured  values  of  g—-,  according  to  Equation  44. 

As  stated  above,  the  curve  for  sodium  chloride  corresponds  with  the 
viscosity  curve  of  pure  water  as  determined  by  Cohen.  It  will  be  seen, 
however,  that  the  curves  for  other  electrolytes  differ  from  that  of  sodium 
chloride  and  that,  therefore,  in  these  cases  the  pressure  effect  upon  the 
ions  is  not  directly  proportional  to  the  viscosity  change  of  the  solution. 
In  the  case  of  potassium  chloride  the  conductance  evidently  increases 
slightly  more  than  corresponds  to  the  viscosity  change  of  the  solution, 
while  for  lithium  chloride  and  hydrochloric  acid  the  conductance  increase 
due  to  increasing  pressure  is  enormously  greater  than  the  viscosity  change 
of  the  solution.  On  the  other  hand,  in  the  case  of  potassium  bromide, 
sodium  bromide,  potassium  iodide,  and  sodium  iodide  the  conductance 
change  of  the  electrolytes  is  much  smaller  than  the  corresponding  vis- 
cosity change  of  the  solution.  Manifestly,  the  change  in  the  speed  of 
the  ions  with  pressure  change  is  dependent  not  only  on  the  viscosity  of 
the  solvent  medium,  but  also  on  other  factors.  What  these  factors  are, 
we  do  not  know  with  certainty,  but  it  appears  probable  that  the  speed 
of  the  ions  is  affected  by  a  change  in  their  effective  size.  Such  an  effect 
will  obviously  be  a  property  of  the  ions  themselves,  which  is  in  accord- 
ance with  Korber's  observations.  However  we  may  interpret  these 
results,  it  is  obvious  that  the  speed  of  the  ions  in  a  dilute  aqueous  solution 
is  not  determined  primarily  by  the  viscosity  of  the  solution,  although  the 
viscosity  is  an  important  factor. 

According  to  Equation  43,  the  value  of  the  ratio  -^L  varies  as  a 
function  of  concentration.  In  Figure  28 *5  are  shown  values  of  the  ratio 
TT-^-  for  sodium  chloride  in  water  at  19.18°  at  a  series  of  concentrations. 

At  the  highest  concentrations  the  resistance  of  the  solution  increases 
throughout  with  increasing  pressure.  This  is  in  accord  with  Cohen's 
observations  on  the  viscosity  of  sodium  chloride  solutions,  which,  at 
higher  concentrations,  exhibit  a  marked  viscosity  increase.  As  the  con- 
centration of  the  solution  decreases,  the  curves  exhibit  a  minimum. 
Initially,  with  increase  in  pressure,  the  resistance  of  the  solution  decreases, 

»*  Korber,  loc.  cit.f  p.  227. 
» Ibid.,  loo.  cit.,  p.  234. 


THE  CONDUCTANCE  OF  SOLUTIONS— VISCOSITIES 


135 


Pressure. 

500     1000     1500    2000    2500    3000  Kg 

Cm- 


0.00ln, 


FIG.  28.    Showing  the  Influence  of  Pressure  on  the  Resistance  of  Sodium  Chloride 
Solutions  at  Different  Concentrations  at  19.18°. 

while  at  higher  pressures  the  resistance  of  the  solution  increases.    In 
this  case,  again,  the  general  form  of  the  curve  corresponds  to  the  viscosity 


136        PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

effects  of  the  solution.  As  the  concentration  decreases,  the  minimum 
point  is  displaced  toward  higher  pressures,  and  the  curves  approach  one 
another.  Thus  the  curves  at  0.1  N  and  0.01  N  differ  but  little.  This  is 
due  to  the  fact  that  below  a  concentration  of  0.1  N  the  ionization  of  the 
electrolyte  is  so  great  and  the  concentration  so  low  that  the  viscosity 
effects  could  not  differ  materially  from  those  in  pure  water.  At  lower 
concentrations,  namely  at  10~3N  and  10~4N,  the  minimum  disappears 
and  the  pressure  effect  becomes  very  large,  the  curves  becoming  the 
steeper,  the  lower  the  concentration  of  the  solution.  This  divergence  of 
the  curves  at  very  low  concentrations  is  due  to  the  effect  of  pressure  on 
the  conductance  of  the  solvent  medium;  namely,  to  the  fourth  term  in 
Equation  43.  In  the  limit,  these  curves  approach  the  dotted  curve  shown 
in  the  figure,  which  is  that  of  the  solvent  medium. 

We  have  still  to  consider  the  case  in  which  the  third  term  of  Equation 
43  becomes  an  effective  factor.  This  will  obviously  be  the  case  with 
solutions  of  weak  electrolytes.  The  ionization  of  an  electrolyte,  if  the 
mass-action  law  holds — and  this  is  in  general  the  case  with  weak  electro- 
lytes in  aqueous  solutions — is  determined  by  the  value  of  its  ionization 
constant  K.  According  to  the  Planck  equation,  we  have: 

(44&)  d  log  £  __       Az; 

dp  RF 

According  to  Tammann,  the  value  of  At>  is  negative,  so  that  as  the  result 
of  pressure  increase  the  value  of  the  ionization  constant  K  increases  and 
with  it  the  value  of  the  ionization  y.  In  the  case  of  weak  electrolytes, 
at  intermediate  concentrations  and  lower  temperatures,  the  first  three 
terms  of  Equation  43  have  the  same  sign,  and  consequently  the  resist- 
ance of  solutions  of  weak  electrolytes  should  decrease  with  increasing 
pressure  much  more  largely  than  that  of  solutions  of  strong  electrolytes 
under  otherwise  the  same  conditions,  and  the  decrease  should  be  the 
greater  the  weaker  the  electrolyte  and  the  greater  the  value  of  Ai>.  The 
first  investigations  in  this  direction  were  carried  out  by  Fanjung.26 
Measurements  on  0.1  N  acetic  acid  were  carried  out  by  Tammann  up  to 
pressures  of  approximately  4000  kilograms  per  square  centimeter.  In 

Rv 

the  following  table  are  given  values  of  the  ratio  -5-*-  for  acetic  acid 

Hp=i 

at  20.140.27 

In  the  case  of  ammonia,  which  has  approximately  the  same  ionization 
constant  as  acetic  acid,  the  pressure  effect  is  even  greater  than  in  that  of 

28 Fanjung,  Ztachr.  1.  pTiys.  Chem.  14.  673  (1894). 
"Tammann,  Wied.  Ann.  69t  770   (1899). 


THE  CONDUCTANCE  OF  SOLUTIONS— VISCOSITIES 


137 


acetic  acid,  since  the  value  of  Av  for  ammonia  is  more  than  twice  that 

of  acetic  acid. 

TABLE   XLVI. 

RELATIVE  RESISTANCE  OF  0.01  N  SOLUTIONS  OP  ACETIC  ACID  IN  WATER 
AT  20.14°  AT  DIFFERENT  PRESSURES. 


cm.2 

1 

500 
1000 
1500 
2000 
2500 
3000 
3500 
4000 


1.000 
0.855 
0.738 
0.650 
0.582 
0.526 
0.487 
0.447 
0.410 


The  influence  of  pressure  upon  the  conductance  of  electrolytes  is 
brought  out  more  clearly  by  representing  the  conductance-pressure  coeffi- 


FIG.  29.    Conductance-Pressure  Coefficients  for  Electrolytes  of  Different  Types  as  a 
Function  of  Concentration  at  a  Pressure  of  500  kg./cm.a. 
Curve  1,  Weak  Electrolytes. 
Curve  2,  Moderately  Strong   Electrolytes. 
Curve  3,  Strong  Electrolytes. 

cient  as  a  function  of  the  concentration  of  the  solution,  the  pressure 
remaining  constant.    In  Figure  29 28  Curve  1  represents  the  pressure 

"Tammann,  Ztachr.  f.  phys.  Chem.  Tl,  729   (1895). 


138        PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

coefficient  of  weak  electrolytes  as  a  function  of  their  concentration  at  a 
pressure  of  500  kg./cm.2  The  curve  actually  corresponds  very  closely  with 
that  of  acetic  acid  in  water  at  this  pressure.  As  Tammann  has  shown, 
it  follows  from  the  Planck  equation  that  at  low  concentrations  and  for 
relatively  small  values  of  the  constant  K  the  ionization  change,  due  to 
increasing  pressure,  increases  with  increasing  concentration,  until  a  prac- 
tically constant  value  is  reached.  The  conductance-pressure  coeffi- 
cient increases  with  increasing  concentration  of  the  weak  electrolyte 
up  to  a  concentration  of  about  10~3  normal  for  electrolytes  whose  con- 
stant is  below  10"*.  At  higher  concentrations  the  ionization  change  due 
to  pressure  change  remains  practically  constant.  However,  at  higher 

concentrations  the  value  of  -  -r—  decreases,  while  the  value  of  —  T^ 

v  Ap  q)  Ap 

decreases  and  ultimately  changes  sign,  as  follows  from  Cohen's  observa- 
tions on  the  viscosity  of  aqueous  salt  solutions.  Therefore,  the  con- 
ductance-concentration curves,  and  consequently  the  curves  for  the  coeffi- 
cient, exhibit  a  very  flat  maximum.  In  the  case  of  solutions  of  strong 

electrolytes,  the  term  --T?  has  inappreciable  values  at  concentrations 

below  10~2  normal,  and  has  only  very  small  values  at  much  higher  con- 
centrations. In  dilute  solutions,  therefore,  the  pressure  coefficient  has 
very  nearly  a  constant  value,  independent  of  concentration.  At  higher 
concentrations,  however,  the  value  of  the  coefficient  decreases,  owing  to 

the  diminution  in  the  value  of  ~T—  and  owing  to  an  ultimate  change  in 

the  sign  of  the  viscosity  effect  at  higher  concentrations  of  the  electrolyte, 
as  was  found  by  Cohen.  Electrolytes  of  intermediate  strength  exhibit 
a  type  of  curve  intermediate  between  these  two  extreme  types,  as  repre- 
sented by  Curve  2.  In  this  case  the  value  of  the  coefficient  increases 
with  increasing  concentration  of  the  solution  at  lower  concentrations 
owing  to  the  increasing  ionization  of  the  electrolyte.  Ultimately,  how- 
ever, the  effect  of  the  viscosity  change  makes  itself  felt,  the  curve  passes 
through  a  maximum,  and  thereafter  falls  with  increasing  concentration. 
At  very  low  concentrations  the  viscosity-pressure  coefficient  has  actually 
been  found  to  increase  and  approach  large  values  due  to  the  effect  of  the 
fourth  term  in  the  right-hand  member  of  Equation  43.  This  increase 
in  the  coefficient,  as  was  shown  by  Tammann,29  is  due  to  the  increased 
ionization  of  the  solvent  medium. 

The  limiting  value  which  the  coefficient  ^-r-  approaches  at  low  con- 

»  Tammann,  Zt&cTvr.  f.  phys.  Chem.  27,  464   (1898). 


THE  CONDUCTANCE  OF  SOLUTIONS—  VISCOSITIES  139 

centrations,  assuming  that  the  conductance  of  the  solvent  is  zero,  or  has 
been  otherwise  corrected  for,  differs  for  different  electrolytes,  and  is,  in 

RP 

general,  the  greater,  the  greater  the  value  of  -5  —  .    Thus  the  limit  ap- 

/tp=i 

preached  for  hydrochloric  acid  at  a  pressure  of  3000  kilograms  per  square 
centimeter  is  approximately  17  per  cent,  while  that  of  sodium  chloride 
is  approximately  8  per  cent  and  that  of  potassium  chloride  9  per  cent. 

Since  in  dilute  solution  the  effect  due  to  -  T-  is  the  same  as  that  in  pure 

v  Ap 

water,  it  follows  that  these  differences  are  due  to  differences  in  the  vis- 
cosity effect  as  illustrated  in  Figure  28.  In  the  case  of  hydrochloric 

acid,  the  value  of  y  -r—  passes  through  a  flat  maximum  at  a  concentration 

in  the  neighborhood  of  0.5  normal. 

In  non-  aqueous  solutions  the  order  of  the  viscosity  effects  differs 
from  that  in  aqueous  solutions,  chiefly  owing  to  the  fact  that  with  in- 
creasing pressure  the  viscosity  of  the  solvent  medium  increases  and  con- 
sequently the  speed  of  the  ions  is  reduced  with  increasing  pressure.  In 

*f> 

Figure  30  30  are  shown  values  of  the  ratio       ^    for  solutions  of  0.002  N 

Kp=i 

tetramethylammonium  iodide  and  0.1  N  malonic  acid  in  ethyl  alcohol. 
As  was  the  case  with  water,  the  curve  for  weak  electrolytes  lies  below 
that  for  strong  electrolytes.  With  increasing  temperature,  however,  the 
order  of  the  curves  is  reversed  with  respect  to  their  order  in  water;  that 

Rv 

is,  the  ratio  decreases  both  in  the  case  of  strong  and  weak  electro- 

Kp=i 

lytes.  The  curves  are  very  nearly  linear  for  solutions  of  strong  electro- 
lytes but  are  convex  toward  the  axis  of  pressures  for  solutions  of  weak 
electrolytes.  This  form  of  the  curve  is  accentuated  in  solutions  in  sol- 
vents of  high  viscosity  ;  as,  for  example,  amyl  alcohol,  for  which  values  of 

Rv 

^—  are  represented  in  Figure  31.31    In  this  case,  the  curves  for  malonic 


acid  at  higher  temperatures  exhibit  a  minimum,  while  the  curves  for 
tetramethylammonium  iodide  are  distinctly  convex  toward  the  axis  of 
pressures.  It  is  evident  that  at  pressures  beyond  3000  kilograms  per 
square  centimeter  the  curve  for  malonic  acid  in  ethyl  alcohol  would 
likewise  pass  through  a  minimum.  The  observed  phenomena  in  non- 


»»  Schmidt,  Ztschr.  f.  phys.  Ghent.  75,  319  (1910). 
11  /bid.,  loc.  cit.f  p.  320. 


140        PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

aqueous  solutions  may  be  accounted  for  in  the  same  manner  as  those  for 
aqueous  solutions.  The  difference  in  the  form  of  the  curves  for  various 
electrolytes  in  the  two  cases  arises  chiefly  as  a  result  of  the  difference 


1.B 
1.7 

1.6 


1.3 


1.0 


0.8 


0.7 


\*> 


60° 


20° 


60° 


1000  2000 

Pressure  in  kg. /cm.2 


JOOO 


FIG.  30.  Showing  the  Influence  of  Pressure  on  the  Resistance  of  0.002  N  Solutions 
of  Tetramethylammonium  Iodide  (above)  and  0.1  Malonic  Acid  (below)  in 
Ethyl  Alcohol  at  Different  Temperatures. 


in  the  sign  and  magnitude  of  the  viscosity  pressure  effect  and  in  the  value 
of  the  ionization  of  the  dissolved  electrolytes.  In  solvents  of  lower 
dielectric  constant,  the  typical  salts  behave  like  electrolytes  of  inter- 
mediate strength.  At  a  given  pressure,  with  increasing  concentration  of 


THE  CONDUCTANCE  OF  SOLUTIONS— VISCOSITIES 

y 


141 


1.0 


C.Q 


60° 


60* 


1000  2000 

Pressure  in  kg./cm.J 


3000 


Fia.  31.  Showing  the  Influence  of  Pressure  on  the  Resistance  of  Solutions  of  Tetra- 
methylammonium  Iodide  (dotted)  and  Malonic  Acid  (continuous)  in  Amyl 
Alcohol  at  Different  Temperatures. 

the  electrolyte,  the  ratio   — ^-,  due  to  the  increased  ionization  of  the 

V1 

electrolyte,  increases  from  values  less  than  unity  to  greater  values  which 
are  in  general  less  than  unity.    At  still  higher  concentrations,  however, 


142        PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

the  increasing  viscosity  effect  overbalances  the  effect  of  increased  ioniza- 
tion and  the  curve  passes  through  a  maximum.  In  solutions  of  weak 

electrolytes  the  ratio  p       increases  rapidly  with  increasing  concentration 

of  the  electrolyte,  due  to  increased  ionization,  and,  for  very  weak  electro- 
lytes, particularly  at  low  temperatures,  passes  through  unity  to  greater 
values.  Here,  again,  at  sufficiently  high  concentrations,  the  curve  may 
pass  through  a  maximum,  owing  to  the  ultimate  predominance  of  the 
viscosity  effect.  From  his  measurements,  making  the  assumption  that 
the  Planck  equation  holds  as  well  as  certain  other  assumptions,  Schmidt 

has  calculated  the  value  of  — — ,  the  viscosity  ratio,  due  to  pressure,  for 

potassium  iodide,  sodium  iodide  and  tetramethylammonium  iodide  in 
alcohol.  He  found  that  this  ratio  increases  markedly  with  the  pressure. 
In  the  case  of  potassium  iodide  and  sodium  iodide  the  increase  is  very 
nearly  the  same,  being  from  1.0  to  2.34  for  0.02  N  solutions  and  a  pres- 
sure change  from  1  to  3000  atmospheres.  In  the  case  of  tetramethyl- 
ammonium iodide  the  ratio  — —  increases  somewhat  more  than  for  the 

other  two  electrolytes  measured.  This  indicates  that  the  viscosity  effect 
in  alcohol,  similar  to  that  in  water,  is  a  property  of  the  ions.  It  appears, 
however,  that  the  effects  in  the  case  of  different  ions  are  much  more 
nearly  the  same  in  non-aqueous  solutions  than  in  water.  This  is  as 
might  be  expected,  since  in  solvents  of  low  dielectric  constant  the  ionic 
conductances  themselves  differ  much  less  than  in  water.  Schmidt  has 
also  calculated  the  value  of  the  ionization  y  at  different  pressures  and 
has  found  that  the  ionization  increases  with  increasing  pressure. 

That  the  pressure  effect  is  intimately  related  to  the  viscosity  of  the 
solution  is  clearly  indicated  by  the  fact  that  the  order  of  the  effects  in 
different  solvents  corresponds  to  the  order  of  the  viscosities  of  these 
solvents.  The  higher  the  viscosity  of  the  solvent,  the  greater  is  the  ratio 

r>—  for  a  given  pressure  change.    In  the  majority  of  solvents  Schmidt 

found  that  this  ratio  might  be  expressed  as  a  function  of  the  pressure  by 
the  equation: 

RV 

(45)  log  •=.  pp} 

where  |3  is  a  constant.  This  equation  was  found  to  be  particularly  ap- 
plicable at  higher  temperatures.  In  other  cases  it  was  necessary  to  add 


THE  CONDUCTANCE  OF  SOLUTIONS-VISCOSITIES  143 

a  quadratic  term  to  the  right-hand  member  of  the  equation.  In  the  case 
of  non-associated  liquids  the  value  of  p  may  be  expressed  in  terms  of 
the  viscosity  of  the  solvent  by  means  of  the  equation: 

(46)  ft  =  0.000106  +  0.00561  cp, 

where  q>  is  the  viscosity  of  the  solvent.  In  the  following  table  are  given 
values  of  the  viscosity  q>,  together  with  the  measured  values  of  p  and 
those  calculated  according  to  Equation  46.32 

TABLE  XLVII. 

RELATION  BETWEEN  THE  VISCOSITIES  OF  DIFFERENT  SOLVENTS  AND 
THE  PRESSURE  EFFECTS. 

Normal  solvents. 
Solvent  (p  p  p  calc. 

Anisaldehyde  0.056  0.03420  0.03420 

Benzylcyanide 0.022  0.03234  0.03229 

Nitrobenzene   0.020  0.03217  0.03218 

Furfurol   0.017  0.03204  0.03201 

Benzaldehyde   0.016  0.03194  0.03196 

Acetic  anhydride 0.010  0.03178  0.03162 

Acetone   0.003  0.03106  0.03123 

Associated  solvents. 

Glycerine 7.0  0.03300  0.0393 

Isoamyl  alcohol 0.042  0.03178  0.03342 

Ethyl  alcohol 0.012  0.03095  0.03173 

Methyl  alcohol 0.006  0.03078  0.03140 

The  calculated  and  observed  values  of  P  agree  very  well  for  the  non- 
associated  solvents,  but  in  the  case  of  the  associate^  solvents  there  is  a 
wide  discrepancy  between  the  two.  A  very  simple  relation  thus  exists 
between  the  viscosity  and  the  pressure  effect  in  the  case  of  normal  sol- 
vents, while  in  the  case  of  associated  solvents  the  relation  is  much  more 
complex.  This  is  as  might  be  expected,  for  in  associated  solvents  a 
change  in  the  complexity  of  the  solvent  molecules  doubtless  accompanies 
any  pressure  change.  It  is  clear  that  the  difference  in  the  nature  of  the 
pressure  effects  in  water  and  in  non-aqueous  solvents  is  chiefly  due  to  the 
difference  in  the  viscosity  effects  in  these  cases. 

w  Schmidt,  loc.  cit.,  p.  334. 


Chapter  VI. 

The  Conductance  of  Electrolytic  Solutions  as  a  Function 

of  Temperature. 

1.  Form  of  the  Conductance-Temperature  Curve.  The  limiting 
value  of  the  conductance  is  a  function  of  the  viscosity  of  the  solvent,  and 
consequently  of  the  temperature  also.  The  conductance  of  the  more 
slowly  moving  ions  is  very  nearly  proportional  to  the  fluidity  of  the 
solvent  over  such  ranges  of  temperature  for  which  viscosity  data  are 
available.  The  conductance  of  the  more  rapidly  moving  ions  increases 
relatively  less  with  the  temperature  than  does  that  of  the  more  slowly 
moving  ions,  and  this  effect  is  the  more  marked  the  greater  the  con- 
ductance of  the  ions. 

In  considering  the  conductance  of  solutions  at  higher  concentrations, 
it  is  necessary  to  take  into  account  another  factor,  namely  the  change 
in  the  ionization  of  the  electrolyte.  The  observed  conductance  change  is 
therefore  the  resultant  effect  due  to  the  change  in  the  viscosity  of  the 
solution  and  to  the  change  in  the  ionization  of  the  electrolyte.  While, 
with  increasing  temperature,  the  viscosity  decreases  and  the  conduct- 
ance consequently  increases,  the  ionization  in  general  decreases  and  the 
conductance  of  the  electrolyte  decreases  in  consequence.  Since  these  two 
factors  affect  the  conductance  in  opposite  directions,  it  follows  that  the 
resultant  effect  of  temperature  on  the  conductance  will  depend  on  the 
relative  magnitude  of  the  ionization  and  the  viscosity  effects;  and,  in 
general,  with  increase  in  temperature  the  conductance  of  a  solution  may 
either  increase  or  decrease.  At  ordinary  temperatures,  the  conductance 
of  many  solutions  increases  with  the  temperature,  and  it  was  formerly 
assumed  that  a  positive  temperature  coefficient  was  a  characteristic 
property  of  electrolytic  solutions.  We  now  know,  however,  that  this  is 
not  the  case  and  that  the  temperature  coefficient  of  solutions  may  be 
either  positive  or  negative  and  that,  in  a  given  solvent,  the  temperature 
coefficient  is  a  function  of  the  temperature  as  well  as  of  concentration, 
and  that  the  sign  of  the  temperature  coefficient  may  change  with  tem- 
perature as  well  as  with  concentration. 

Considering,  first,  the  conductance  as  a  function  of  temperature,  the 
concentration  remaining  fixed,  it  is  found  that,  in  general,  the  con- 
ductance increases  with  the  temperature  at  low  temperatures;  but  as  the 

144 


SOLUTIONS  AS  A  FUNCTION  OF  TEMPERATURE 


145 


temperature  rises,  the  temperature  coefficient  decreases.  The  conductance 
curve  is  therefore  concave  toward  the  axis  of  temperatures.  If  the  tem- 
perature is  carried  sufficiently  high,  the  conductance  passes  through  a 
maximum  after  which  it  decreases,  the  negative  temperature  coefficient 
increasing  as  the  temperature  rises.  Experiments  of  this  kind  were  first 
carried  out  by  Sack,1  who  found  that,  in  solutions  of  copper  sulphate, 


-60      ' 


O        2O       46  %     6O      6O      /OO 

Temperature. 


FIG.  32.    Conductance-Temperature  Curves  for  Various  Electrolytes  in 
Liquid  Ammonia. 

the  conductance  passes  through  a  maximum  in  the  neighborhood  of  128°. 
For  solutions  of  strong  binary  electrolytes  in  water,  however,  the  maxi- 
mum lies  at  much  higher  temperatures. 

Before  proceeding  to  a  detailed  discussion  of  aqueous  solutions,  we 
may  consider  solutions  in  other  solvents.  The  conductances  of  a  con- 
siderable number  of  solutions  in  ammonia  have  been  measured  and  a 
maximum  has  been  found  in  all  cases.2  The  form  of  the  curves  will  be 

*Sack,  Wied.  Ann.  d.  Phys.  tf,  212  (1891). 

2  Franklin  and  Kraus,  Am.  Chem.  J.  tk,  83   (1900). 


146        PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

evident  from  Figure  32.  As  a  rule  the  maximum  lies  in  the  neighborhood 
of  25°  C  but  the  temperature  of  the  maximum  is  a  function  of  concen- 
tration and  with  increasing  concentration  the  maximum  is  displaced 
toward  lower  temperatures.  The  curves  for  different  electrolytes  are 
similar,  indicating  that  the  underlying  phenomenon  is  the  same  in  all 
cases.  As  the  critical  temperature  is  approached,  the  conductance  ap- 
proaches a  very  low  value,  and  it  appears  as  though  the  curve  would  cut 
the  axis  of  temperatures  at  a  point  near  the  critical  temperature.  The 
conductance,  however,  does  not,  in  fact,  fall  to  zero  at  the  critical  point, 
but  has  appreciable  values  at  temperatures  much  above  that  point.  The 
phenomenon  in  the  neighborhood  of  the  critical  point  will  be  discussed 
in  detail  in  another  section  and  need  not  be  further  considered  here.  It 
may  be  stated,  however,  that  the  property  of  forming  conducting  solu- 
tions with  electrolytes  is  not  peculiar  to  the  liquid  state  but  is  one  com- 
mon to  fluid  systems. 

The  .form  of  the  conductance-temperature  curve  is  the  same  in  all  sol- 
vents. The  conductance  of  a  considerable  number  of  solutions  in  sul- 
phur dioxide  has  been  measured  3  at  higher  temperatures  and  the  curves 
obtained  have  a  form  which  corresponds  with  those  of  ammonia  solu- 
tions. In  solutions  of  KI  in  methylamine  the  form  of  the  curve  differs 
slightly  in  that,  at  very  high  temperatures,  the  conductance  appears  to 
approach  the  axis  of  temperatures  asymptotically.  In  the  alcohols,4 
as  well  as  in  water,5  the  conductance-temperature  curves  are  of  the  same 
general  type. 

2.  Conductance  of  Aqueous  Solutions  at  Higher  Temperatures. 
In  order  to  proceed  with  the  discussion  of  this  subject,  it  is  necessary  to 
have  some  notion  as  to  the  degree  of  ionization  of  the  electrolyte  in  solu- 
tion. The  degree  of  ionization  of  non-aqueous  solutions  at  higher  tem- 
peratures is  unknown.  In  other  words,  we  do  not  have  a  sufficient  num- 
ber of  measurements  at  a  series  of  temperatures  and  concentrations  to 
enable  us  to  determine  the  value  of  A0  at  these  temperatures.  For 
aqueous  solutions,  however,  a  large  amount  of  material  is  available, 
having  been  obtained  by  A.  A.  Noyes  and  his  associates,6  and  from  these 
data  the  effect  of  temperature  on  the  ionization  of  salts  becomes  ap- 
parent. 

In  the  following  table  are  given  values  of  the  equivalent  conductance 
for  potassium  chloride  at  a  series  of  temperatures  and  at  the  concentra- 
tions 0.08  and  0.002  normal. 

1  Walden  and  Centnerszwer,  ZtscTir.  }.  phys.  Chem.  39,  542  (1902) 
«Kraus,  Phy8.  Rev.  18,  40  and  89   (1904). 
8  Noyes,  Carnegie  Publication,  No.  63,  pp.  47,  103,  and  266. 
•Noyes,  loc.  cit. 


SOLUTIONS  AS  A  FUNCTION  OF  TEMPERATURE  147 

TABLE  XLVIII. 
CONDUCTANCE  OF  KC1  IN  H20  AT  HIGHER  TEMPERATURES. 

Concentration  *  0°  18°  25°  100°  140°  156°  218°  281°  306° 
0.08  N.  A  72.3  113.5  —  341.5  455  498  638  723  720 

0.002  N.  A    79.6     126.3     146.4     393    534    588    779    930     1008 

It  will  be  noted  that  at  the  higher  concentration  the  conductance  passes 
through  a  maximum  somewhere  between  281°  and  306°.  In  the  more 
dilute  solution,  a  maximum  has  not  been  reached  below  306°.  This 
behavior  is  quite  general  in  aqueous  solutions  and  is  found  also  in  non- 
aqueous  solutions.  The  lower  the  concentration,  the  higher  the  tem- 
perature of  the  maximum. 

For  solutions  of  sodium  chloride,  the  conductance-temperature  curve 
is  similar  to  that  of  potassium  chloride,  although  for  this  salt  the  maxi- 
mum has  not  been  reached  at  306°,  even  at  a  concentration  of  0.08 
normal.  We  have  seen  that,  with  increasing  temperature,  the  conduct- 
ance of  the  sodium  ion  increases  relatively  more  than  that  of  the  potas- 
sium ion.  As  a  consequence,  the  maximum  in  the  conductance  curve  is 
shifted  to  higher  temperatures.  In  general,  the  higher  the  conductance 
of  the  electrolyte,  the  lower  the  temperature  of  the  maximum  and  the 
lower  the  concentration  at  which  the  maximum  will  appear  at  a  given 
temperature. 

For  silver  nitrate,  the  maximum  lies  somewhat  lower  than  it  does  for 
potassium  chloride,  as  may  be  seen  from  the  following  table: 

TABLE   XLIX. 
CONDUCTANCE  OF  AgN03  IN  H20  AT  HIGH  TEMPERATURES. 

Concentration        t       18°  100°         156°         218°         281°         306° 

0.08  N  A      96.5          294          432          552          614          604 

The  lower  temperature  of  the  maximum  for  silver  nitrate  is  due,  partly, 
to  the  abnormal  manner  in  which  the  conductance  of  the  nitrate  ion 
changes  as  a  function  of  the  temperature  and,  partly,  to  the  more 
rapid  decrease  in  the  ionization  of  silver  nitrate  with  increasing  tem- 
perature. 

The  higher  types  of  salts  exhibit  maxima  which  are  more  pronounced 
and  which  occur  at  lower  concentrations  and  lower  temperatures.  In 
Table  L  are  given  values  for  barium  nitrate  and  magnesium  sulphate  at 
0.08  normal. 


148        PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

TABLE   L. 
CONDUCTANCE  OF  Ba(N03)2  AND  MgS04  IN  H20  AT  HIGH  TEMPERATURES. 

Barium  Nitrate. 

Concentration  Temp.        18°          100°          156°        218°        281° 
0.08  N  A  81.6        257.5        372          449          430 

Magnesium  Sulphate. 

Temp.         18°  100°  156°  218° 

0.08  N  A  52    •«.  136  133  75.2 

It  will  be  observed  that  the  maximum  lies  below  281°  for  barium  nitrate, 
while  for  magnesium  sulphate  the  maximum  lies  between  100°  and  156°. 
The  more  complex  the  salt  the  lower  the  temperature  and  the  lower  the 
concentration  at  which  the  maximum  appears.  As  we  shall  see  presently, 
this  is  due  chiefly  to  the  fact  that  the  ionization  of  salts  of  higher  type 
falls  off  more  rapidly  with  the  temperature  than  does  that  of  the  binary 
salts.  For  strong  acids,  the  maxima  lie  at  temperatures  considerably 
below  those  of  the  binary  salts.  For  hydrochloric  acid  the  maximum 
lies  in  the  neighborhood  of  240°  and  for  nitric  acid  in  the  neighborhood 
of  200°  at  a  concentration  of  0.08  N. 

The  conductance-temperature  curve  of  sulphuric  acid,  which  is  a 
dibasic  acid,  has  a  peculiar  form,  which  has  an  important  significance. 
Below  are  given  values  of  the  equivalent  conductance  for  sulphuric  acid 
at  a  series  of  temperatures  at  concentrations  0.002  and  0.08  normal. 

TABLE  LI. 
CONDUCTANCE  OF  H2S04  AT  HIGH  TEMPERATURES. 

Concentration  18°  25°  50°  75°  100°  128°  156°  218°  306° 
0.002  N  353.9390.8  501.3  560.8  571.0  551  536  563  637 

0.08  N  240     258       306       342       373       408    440    488    474 

It  will  be  observed  that,  at  the  higher  concentration,  sulphuric  acid 
exhibits  a  relatively  flat  maximum  at  a  temperature  of  about  250°,  while 
at  the  lower  concentration  it  exhibits  a  maximum  at  about  100°  and  a 
minimum  at  about  160°,  after  which  the  conductance  again  increases 
and  presumably  passes  through  a  maximum  at  a  temperature  above  306°. 
At  still  lower  concentration  the  maxima  and  minima  become  more  pro- 
nounced. As  Noyes  and  Eastman 7  pointed  out,  this  behavior  of  sul- 
phuric acid  appears  to  be  due  to  the  fact  that  ionization  takes  place  in 
two  stages  according  to  the  equations: 

*  Noyes,  Joe.  cit.,  p.  270. 


SOLUTIONS  AS  A  FUNCTION  OF  TEMPERATURE  149 

H2S04  =  H+  +  HS04- 
HS04-  =  H+  +  S04- 

At  the  higher  concentrations,  the  second  ionization  process  has  taken 
place  to  only  a  small  extent  and  the  form  of  the  curve  is  largely  due  to 
the  change  in  the  ionization  according  to  the  first  process,  the  maximum 
point  occurring  when  the  increased  conductance  of  the  ions  due  to  tem- 
perature is  just  counterbalanced  by  the  decreased  conductance  due  to 
decrease  in  ionization.  At  the  lower  concentration  the  second  ionization 
process  is  likewise  involved.  The  second  ionization  corresponds  to  that 
of  the  weaker  acid  and  the  ionization  according  to  this  process  falls  off 
more  rapidly  with  rising  temperature,  thus  giving  rise  to  the  initial 
maximum.  When  the  ionization  according  to  the  second  process  has 
been  largely  depressed,  the  curve  thereafter  depends  chiefly  upon  the 
ionization  according  to  the  first  equation. 

The  ionization  of  strong  electrolytes,  apparently  without  exception, 
decreases  with  increasing  temperatures;  but  at  lower  temperatures  the 
rate  of  decrease  is  relatively  small.  In  the  case  of  the  weak  acids  and 
bases  the  ionization  increases  between  0°  and  40°,  and  thereafter  de- 
creases rapidly  at  higher  temperatures.  In  the  following  table  are  given 
values  for  the  ionization  constants  of  ammonium  hydroxide  and  acetic 
acid.8  The  values  represent  averages  for  a  number  of  concentrations. 
In  general,  the  ionization  constant  is  independent  of  concentration  up 
to  0.1  normal. 

TABLE  LII. 

IONIZATION  CONSTANT  X  10~8  FOB  AMMONIUM  HYDROXIDE  AND 

ACETIC  ACID. 


18°  25°  218°  306° 

NH4OH    17.2  18.1  1.80  0.093 

CH3COOH 18.3  1.72  0.139 

Initially  there  is  a  slight  increase  in  the  ionization  constant,  after 
which  there  is  a  sharp  decrease  at  higher  temperatures.  Between  218° 
and  306°  the  constant  of  ammonium  hydroxide  changes  slightly  more 
than  that  of  acetic  acid.  Similar  results  have  been  obtained  in  the  case 
of  other  weak  acids.  For  example,  the  ionization  constant  of  diketo- 
tetrahydrothiazole 9  at  0°,  18°  and  25°  is  respectively  0.0711  X  10'6, 
0.146  X  10-6  and  0.181  X  10~6.  Between  0°  and  25°  the  constant  of  am- 
monium hydroxide  varies  between  13.91  and  18.06  X  10~6.  It  appears 

•  Noyes,  Joe.  tit.,  p.  234. 

•  /bid.,  Joe.  cit.,  p.  290. 


150        PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

that  the  change  in  the  value  of  the  constant  is  greater  for  the  weaker 
electrolyte. 

The  ionization  constant  for  water  itself  is  a  function  of  the  tem- 
perature. At  ordinary  temperature  the  constant  has  been  variously 
determined,  the  values  at  18°  lying  between  0.68  and  0.80,  the  lower 
value  being  probably  the  more  nearly  correct. 

In  the  following  table  are  given  values  of  the  ionization  constant  of 
water  at  various  temperatures  up  to  306 °.10 

TABLE  LIII. 
IONIZATION  CONSTANT  OF  WATER  AT  DIFFERENT  TEMPERATURES. 

0°  18°         25°         100°         156°        218°        306° 

KWX  1014  ...  0.089        0.46        0.82        48.          223.         461.         168. 

The  ionization  constant  of  water  thus  increases  very  rapidly  at  lower 
temperatures  and  passes  through  a  maximum  not  far  from  218°.  The 
large  value  of  the  ionization  constant  of  water  and  the  relatively  low 
values  of  the  ionization  constants  of  the  acids  and  bases  at  higher  tem- 
peratures lead  to  a  relatively  large  hydrolysis  of  the  salts  of  anything 
but  the  strongest  acids  and  bases,  and  it  is  not  improbable  that  even 
salts  of  the  strong  acids  and  bases  ultimately  suffer  hydrolysis  at  low 
concentrations  at  the  highest  temperatures. 

The  increase  in  the  ionization  constant  of  the  weak  acids  between 
0°  and  40°  may  be  related  to  the  molecular  changes  which  water  under- 
goes within  this  temperature  interval.  Within  this  interval  the  density 
and  specific  heat  of  water  are  abnormal  and  within  this  temperature 
interval,  also,  the  viscosity  effects  in  solution,  as  well  as  the  viscosity 
effects  under  pressure,  exhibit  abnormal  relations,  as  has  already  been 
pointed  out.  An  adequate  explanation  of  these  various  phenomena,  how- 
ever, appears  not  to  exist. 

The  ionization  of  different  electrolytes  in  water  at  temperatures  from 
18°  to  306°  are  given  in  Table  LIV  at  concentrations  of  0.01  and  0.08 
normal.  An  examination  of  this  table  shows  that  the  ionization  of  all 
electrolytes  decreases  markedly  with  the  temperature,  the  decrease  being 
the  greater  the  higher  the  temperature  and  the  higher  the  concentration. 
The  ionization-temperature  curves  of  different  binary  electrolytes  corre- 
spond closely  with  one  another,  with  the  exception  of  the  strong  acids 
and  silver  nitrate.  In  the  case  of  the  last  named  salt,  however,  the 
ionization  values  at  the  highest  temperatures  are  subject  to  large  errors, 

10  Noyes,  loc.  cit.,  p.  346. 


SOLUTIONS  AS  A  FUNCTION  OF  TEMPERATURE 


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152        PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

owing  to  the  possible  hydrolysis  of  the  salt,  as  well  as  to  certain  reactions 
which  appear  to  take  place  in  the  solutions  at  the  higher  temperatures.11 
The  ionization  of  hydrochloric  and  nitric  acids  falls  off  much  more 
rapidly  than  does  that  of  the  salts  and  that  of  nitric  acid  falls  off  more 
rapidly  than  that  of  hydrochloric  acid,  as  may  be  seen  from  Table  LIV. 
At  0.08  normal  and  306°,  the  ionization  of  nitric  acid  is  only  about  one 
half  that  of  hydrochloric  acid.  At  that  temperature  .the  ionization  of 
hydrochloric  acid  is  approximately  the  same  as  that  of  the  typical  binary 
salts,  such  as  potassium  and  sodium  chlorides.  The  ionization  of  weak 
electrolytes,  such  as  ammonium  hydroxide  and  acetic  acid,  falls  off  much 
more  rapidly  than  does  that  of  the  strong  electrolytes.  Correspondingly, 
at  a  given  concentration,  the  maximum  in  the  conductance-temperature 
curves  occurs  at  lower  temperatures  in  the  case  of  weak  acids  and  bases. 
For  acetic  acid  this  maximum  lies  in  the  neighborhood  of  100°. 

The  ionization  of  salts  of  higher  type,  as  well  as  that  of  the  more 
complex  acids  and  bases,  such  as  sulphuric  acid  and  barium  hydroxide, 
falls  off  very  markedly  with  the  temperature,  and  the  decrease  is  as  a 
rule  the  greater  the  higher  the  type  of  the  salt.  This  is  well  illustrated 
in  the  case  of  magnesium  sulphate,  whose  ionization  at  0.08  normal  and 
218°  is  only  7  per  cent.  Corresponding  to  this  rapid  decrease  in  the 
ionization  of  the  more  complex  salts  at  the  higher  temperatures,  the 
maximum  in  the  conductance  curves  lies  at  relatively  low  temperatures. 

As  the  temperature  rises,  the  dielectric  constant  of  water  decreases 
and  we  should  expect  the  properties  of  aqueous  solutions  to  approach 
those  of  non-aqueous  solutions.  This  is  indeed  the  case.  At  higher  tem- 
peratures, the  ionization  values  for  different  electrolytes  approach  those 
of  the  same  type  of  electrolytes  in  solvents  of  lower  dielectric  constants. 
The  low  ionization  values  of  the  salts  of  higher  type  correspond  with 
the  relatively  low  values  of  the  ionization  of  the  same  type  of  salts  in 
nearly  all  non-aqueous  solvents.  At  306°,  many  of  the  properties  of 
electrolytic  aqueous  solutions,  which  differentiate  these  solutions  from 
similar  solutions  in  non-aqueous  solvents,  have  in  large  measure  dis- 
appeared. So,  for  example,  the  great  difference  in  the  conductance 
values  of  the  different  ions  has  almost  completely  disappeared  at  306°. 
Similarly  the  abnormally  high  ionization  values  of  hydrochloric  and 
nitric  acids,  as  well  as  of  the  strong  bases,  have  disappeared  at  this 
temperature.  And,  finally,  the  ionization  function,  for  the  binary  elec- 
trolytes at  any  rate,  approaches  values  not  very  different  from  those  of 
solutions  in  many  non-aqueous  solvents. 

It  is  evident  that,  since  the  ionization  decreases  with  the  temperature, 

u  Noyes,  loc.  cit.,  p.  94. 


SOLUTIONS  AS  A  FUNCTION  OF  TEMPERATURE  153 

the  value  of  the  ionization  function  likewise  decreases.  It  is  interesting 
to  examine  the  general  course  of  the  ionization  function  at  different 
temperatures.  In  the  following  table  are  given  values  of  the  ionization 
function  K'  at  a  series  of  concentrations  at  156°  and  306°,  for  potassium 
chloride,  and  at  156°,  218°  and  306°  for  nitric  acid. 

TABLE   LV. 

VALUES  OF  THE  IONIZATION  FUNCTION  Kf  FOR  STRONG  ELECTROLYTES  IN 
WATER  AT  HIGHER  TEMPERATURES. 

Potassium  Chloride. 

C  X  103  0.5  2.0  10.  80.          Temp. 

K'  X  102  2.68  5.67  18.9  39.6  156° 

0.882  13.0  306° 

Nitric  Acid. 

CX103  0.5  2.0  10.  80.  Temp. 

K'  X  102  2.68  4.87  10.7  28.0  156° 

1.57  3.53  8.30  21.6  218° 

0.60  1.22  2.96  8.53  306° 

Allowance  must,  of  course,  be  made  for  the  more  or  less  continuous 
increase  in  the  probable  error  of  the  conductance  values  as  the  tem- 
perature rises.  The  uncertainty  in  the  value  of  the  ionization  function 
K',  however,  probably  does  not  increase  in  the  same  proportion,  since, 
at  a  given  concentration  the  ionization  of  the  salt  decreases  with  tem- 
perature, and  a  given  percentage  error  in  A  or  A0  has  as  a  consequence 
a  smaller  percentage  error  in  the  value  of  K'.  At  the  higher  concentra- 
tions, at  any  rate,  the  values  of  K'  are  approximately  correct.  In  the 
case  of  potassium  chloride  at  156°,  the  general  course  of  the  curve  is 
similar  to  that  of  potassium  chloride  at  18°,  but  the  value  of  the  function 
is  somewhat  lower.  At  306°,  the  value  of  the  function  K'  is  markedly 
lower  than  at  156°.  Thus,  at  0.08  normal,  between  156°  and  306°,  K' 
changes  from  0.396  to  0.13.  Correspondingly,  at  lower  concentrations 
the  value  of  the  function  K'  becomes  much  smaller.  The  change  in  the 
value  of  the  function  K'  is  most  marked  in  the  case  of  nitric  acid.  For 
this  electrolyte,  between  156°  and  306°,  the  value  of  K'  decreases  ap- 
proximately in  the  ratio  of  1  to  4.  For  hydrochloric  acid  the  change  in 
the  value  of  K'  is  much  smaller  than  it  is  for  nitric  acid.  Since,  at 
306°,  the  ionization  curve  of  hydrochloric  acid  differs  but  little  from  that 
of  potassium  chloride,  it  is  obvious  that  the  value  of  the  function  K'  for 
hydrochloric  acid  is  approximately  the  same  as  for  potassium  chloride 
at  that  temperature.  At  18°  and  0.1  N,  the  value  of  K'  is  0.5  for  potas- 


154        PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

slum  chloride  and  1.1  for  nitric  acid.  '  It  is  evident  that  at  the  higher 
temperatures  the  strong  acids  and  bases  are  relatively  much  weaker 
than  at  lower  temperatures. 

Owing  to  uncertainties  in  the  conductance  values  and  the  meagreness 
of  the  experimental  material  at  the  higher  temperatures,  it  is  not  possible 
to  determine  whether  or  not  the  mass-action  law  actually  is  approached 
as  a  limiting  form  in  the  case  of  aqueous  solutions;  but  it  seems  not 
unlikely  that  such  is  the  case.  In  view  of  the  high  value  of  the  ioniza- 
tion  constant  of  water  and  the  relatively  low  value  of  the  ionization 
function  of  the  acids  and  bases  at  higher  temperatures,  it  follows  that  at 
these  temperatures  typical  salts  will  be  hydrolyzed  to  an  appreciable 
extent  in  dilute  solutions  and  that  salts  of  slightly  weaker  acids  and 
bases,  and  particularly  of  the  polybasic  acids  and  the  polyacid  bases, 
undergo  appreciable  hydrolysis. 

3.  The  Conductance  of  Solutions  in  N on- Aqueous  Solvents  as  a 
Function  of  the  Temperature.  In  aqueous  solutions,  the  maxima  of  the 
temperature-conductance  curves  lie  at  temperatures  which  are  the  lower 
the  higher  the  concentration  of  the  solution.  The  observed  conductance 
change  with  rising  temperature  is  the  resultant  effect  of  an  increase  in 
conductance  due  to  increasing  fluidity  of  the  solvent,  and  a  decrease, 
due  to  decreasing  ionization  of  the  salt.  In  very  dilute  solutions,  where 
the  ionization  is  approaching  unity  in  all  cases,  the  conductance  in- 
creases with  the  temperature  at  all  temperatures,  since  the  ionization 
remains  practically  fixed  in  the  neighborhood  of  unity,  while  the  fluidity 
of  the  solvent  increases.  At  higher  concentrations,  the  ionization  de- 
creases with  the  temperature  and  presumably,  at  sufficiently  high  tem- 
peratures, it  decreases  at  a  sufficient  rate  to  overcome  the  increase  in 
conductance  due  to  the  fluidity  change  of  the  solvent.  When  the  two 
effects  balance,  the  temperature  coefficient  becomes  ze^p,  while  at  higher 
concentrations  the  temperature  coefficient  becomes  negative. 

In  non-aqueous  solutions,  particularly  in  solvents  of  low  dielectric 
constant,  the  temperature-conductance  curves,  as  functions  of  the  con- 
centration, have  a  somewhat  different  form.  In  very  dilute  solutions, 
where  the  ionization  is  great,  the  conductance  increases  with  the  tem- 
perature because  of  the  increasing  fluidity  of  the  solvent.  At  certain 
intermediate  concentrations  and  above  certain  temperatures,  the  con- 
ductance decreases  with  the  temperature,  although  at  much  lower  tem- 
peratures the  curve  in  general  passes  through  a  maximum.  At  much 
higher  concentrations,  that  is,  in  the  neighborhood  of  normal  and  above, 
the  temperature  coefficient  is  again  throughout  positive;  that  is,  the 
conductance  increases  with  the  temperature  at  all  temperatures.  In  the 


SOLUTIONS  AS  A  FUNCTION  OF  TEMPERATURE  155 

following  table  are  given  values  of  the  conductance  of  potassium  iodide 
and  ammonium  sulphocyanate  in  S02  at  temperatures  from  — 33°  to 
+  10°.12 

TABLE  LVI. 

CONDUCTANCE  OF  ELECTROLYTES  IN  S02  AT  DIFFERENT  TEMPERATURES. 

Potassium  Iodide. 
V  —33°          —20°          —10°  0°  +10° 

1.00  37.7  44.1  46.9  51.2  54.5 

128.0  65.9  66.9  66.5  64.5  62.0 
4000.                139.0            151.0            162.5            166.3            168.7 

Ammonium  Sulphocyanate. 

1.28  9.42  10.17  10.82  11.13  11.33 

167.1  17.01  16.44  15.92  15.10  14.01 

It  will  be  observed  that  in  the  neighborhood  of  normal  the  con- 
ductance curve  for  both  salts  rises  throughout  with  increasing  tempera- 
ture. In  the  neighborhood  of  0.01  normal  there  is  a  slight  increase 
between  — 33°  and  — 20°  in  the  case  of  potassium  iodide,  after  which 
the  conductance  decreases  throughout  with  the  temperature.  At  the 
lo'wer  concentration,  the  conductance  of  ammonium  sulphocyanate  de- 
creases throughout  with  increasing  temperature.  At  a  dilution  of  four 
thousand  liters,  the  conductance  of  potassium  iodide  increases  throughout 
with  increasing  temperature. 

The  effect  of  temperature  on  the  conductance  of  solutions  in  non- 
aqueous  solvents  is  readily  interpreted  in  terms  of  Equation  11.  What 
we  have  to  consider  is  the  influence  of  temperature  upon  the  constants 
of  this  equation.  We  have  seen  that  as  the  dielectric  constant  of  the 
solvent  decreases,  Ce.,  as  the  temperature  rises,  the  value  of  the  constant 
K  decreases  and  ultimately  reaches  very  low  values.  On  the  other  hand, 
as  the  dielectric  constant  decreases,  the  exponent  m  increases  while  the 
constant  D  remains  practically  independent  of  the  dielectric  constant  of 
the  solvent.  If  the  mass-action  constant  K  is  not  too  small,  then,  at  high 
dilutions,  the  ionization  of  the  electrolyte  will  approach  unity,  whatever 
the  dielectric  constant  of  the  solvent.  It  follows,  therefore,  that  with 
increasing  temperature  the  conductance  of  such  dilute  solutions  will 
increase  throughout  as  the  temperature  increases.  The  constant  D,  as 
we  have  seen,  determines  the  value  of  the  ionization  at  very  high  con- 
centrations. At  unit  ion  concentration  the  value  of  the  ionization  is 

"Franklin,  J.  PJiys.  Chem.  15,  675   (1911). 


156       PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

Y'  =  T~j~ry    F°r  strong  electrolytes  D  has  a  value  in  the  neighborhood 

of  0.35.  The  ionization  at  this  concentration  is  therefore  0.26  and  the 
concentration  of  the  salt  at  this  ion  concentration  is  accordingly  in  the 
neighborhood  of  4.0  normal.  If  the  constant  D  is  independent  of  tem- 
perature, then  the  ionization  at  this  concentration  will  remain  fixed  and 
consequently,  with  increasing  temperature,  the  conductance  of  the  solu- 
tion will  increase  throughout,  since  the  fluidity  of  the  solution  increases 
with  increasing  temperature.  At  very  high  and  at  very  low  concentra- 
tions, therefore,  the  conductance  of  all  solutions  should  increase  with 
increasing  temperature.  At  intermediate  concentrations,  the  ionization 
decreases  as  the  dielectric  constant  decreases ;  that  is,  as  the  temperature 
increases.  The  decrease  in  the  ionization  in  this  region  is  largely  deter- 
mined by  the  decrease  in  the  value  of  the  constant  K  and  increase  in 
the  value  of  the  exponent  ra.  For  higher  values  of  the  dielectric  con- 
stant and  for  salts  having  a  high  value  of  the  constant  K  and  low  value 
of  the  constant  D  and  a  value  of  the  exponent  m  less  than  1,  the  change 
of  the  constants  m  and  K  has  relatively  a  small  effect  upon  the  value  of 
the  ionization  at  intermediate  concentrations.  As  a  result,  at  low  tem- 
peratures, or  rather,  for  values  of  the  dielectric  constant  greater  than 
about  20,  the  ionization  changes  but  little  as  the  temperature  increases 
and  such  solutions  exhibit  a  positive  temperature  coefficient  over  the 
entire  range  of  concentration.  When,  however,  the  dielectric  constant 
falls  below  a  value  in  the  neighborhood  of  20,  the  exponent  m  increases 
markedly  and  the  constant  K  decreases  largely  with  temperature.  Con- 
sequently, at  intermediate  concentrations,  the  decrease  in  the  ionization 
more  than  compensates  for  the  increase  in  the  conductance  due  to  the 
increased  fluidity  of  the  solutions.  The  conductance  of  solutions  at  such 
intermediate  concentrations,  therefore,  decreases  with  increasing  tem- 
perature. 

In  order  to  illustrate  the  effect  of  temperature  upon  the  conductance 
of  solutions,  ionization  and  conductance  curves  have  been  calculated  for 
an  electrolyte  having  the  constants  given  in  the  following  table: 

TABLE  LVIL 

ASSUMED  CONSTANTS  OF  EQUATION  11  TO  ILLUSTRATE  THE  EFFECT  OF 
TEMPERATURE  ON  CONDUCTANCE. 

t  A0  XX  10*  m  D 

+  10°  240                  5.2  1.21  0.4 

—  10°  200                 8.5  1.14  0.4 

—  30°  160                13.0  1.05  0.4 

—  50°  120               20.0  0.95  0.4 


SOLUTIONS  AS  A  FUNCTION  OF  TEMPERATURE 


157 


These  constants  correspond  very  nearly  with  those  for  solutions  of  potas- 
sium iodide  in  sulphur  dioxide.  The  data  for  these  solutions  present 
certain  inconsistencies,  particularly  at  low  concentrations,  which  render 
it  very  difficult  to  determine  the  precise  values  of  A<>.  Accordingly,  the 
approximate  constants  given  above  have  been  adopted  for  the  purpose 
of  illustrating  the  effect  of  temperature  upon  the  ionization  and  con- 
ductance of  an  electrolyte.  The  constant  D  is  assumed  to  be  inde- 
pendent of  temperature.  This  condition  is  approximately  fulfilled  in 
solvents  having  dielectric  constants  lower  than  25.  The  lower  curves 


Z25 
ZOO 
175 


,00 


75 


50 


45 


£•0 


£00 


ISO     § 


100 


so 


1.0 


0.0 


T.o 


3.0 


Log  V. 

FIG.  33.    Illustrating  the  Influence  of  Temperature  on  the  Ionization  and  the  Con- 
ductance of  Electrolytes  in  Solvents  of  Relatively  Low  Dielectric  Constant. 

in  Figure  33  represent  the  values  of  the  ionization  at  different  tempera- 
tures, the  lower  curves  corresponding  to  the  higher  temperatures.  In 
order  to  secure  a  plot  on  which  the  ionization  and  conductance  values 
may  be  conveniently  represented  at  all  concentrations,  the  logarithms  of 
the  concentrations,  instead  of  the  concentrations  themselves,  have  been 
plotted  as  abscissas.  It  will  be  observed  that  the  ionization  curves  inter- 
sect at  a  concentration  of  3.6  normal,  corresponding  to  the  value  log 
C  =  0.556.  Actually,  the  intersections  do  not  occur  at  a  point,  since  the 

I 


ionization  is  given  by  the  equation  y  = 


, 
JD  -f- 


and  the  constant  K 


158        PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

decreases  slightly  as  the  temperature  increases.  The  value  of  K,  how- 
ever, is  so  small  that  this  effect  is  scarcely  appreciable.  At  concentra- 
tions greater  than  3.6  normal,  the  ionization  increases  with  the  tempera- 
ture, and  this  increase  is  the  greater  the  greater  the  value  of  m.  In 
general,  the  increased  conductance  due  to  increased  ionization  in  these 
regions  is  masked  by  the  rapidly  increasing  effects  of  viscosity.  In  the 
'  neighborhood  of  normal  concentration  the  viscosity  effect  becomes  suffi- 
ciently great  to  overbalance  the  conductance  increase  due  to  increased 
ionization  and  the  conductance-temperature  curves  pass  through  a  maxi- 
mum in  this  region,  after  which  they  fall  off  very  rapidly.  Nevertheless, 
it  is  to  be  noted  that,  in  all  cases  for  which  measurements  are  available 
at  different  temperatures  in  very  concentrated  solutions,  the  conductance 
increases  markedly  with  the  temperature  and  this  increase  is  the  greater 
the  higher  the  concentration.  In  Table  LVIII  are  given  values  of  the 
conductance  of  concentrated  solutions  of  different  salts  in  methylamine 
and  ethylamine  at  a  series  of  temperatures.13 

What  is  striking  in  these  results  is  the  high  value  of  the  temperature 
coefficient  at  high  concentration,  as,  for  example,  in  solutions  of  silver 
nitrate  in  methylamine  at  V  =  0.2456.  Between  —33.5°  and  —15° 
the  conductance  increases  91  per  cent  or  4.92  per  cent  per  degree.  The 
same  holds  true  for  solutions  of  silver  nitrate  in  ethylamine,  where  the 
conductance  increases  nearly  100  per  cent  between  — 33.5°  and  — 15° 
at  0.4083  N,  while,  between  — 15°  and  0°,  the  conductance  of  solutions 
of  ethylammonium  chloride  increases  6.76  per  cent  per  degree  at  0.17  N. 
It  is  true  that  the  viscosity  in  these  concentrated  solutions  must  differ 
greatly  from  that  of  the  solvent  and  the  viscosity  may  change  much 
more  rapidly  with  the  temperature  in  the  case  of  the  concentrated  solu- 
tions than  in  that  of  the  more  dilute  solutions.  Nevertheless,  it  appears 
not  improbable  that  the  high  value  of  the  temperature  coefficients  of 
concentrated  solutions  is  in  part  due  to  the  increased  ionization  at  these 
high  concentrations. 

As  the  concentration  decreases  below  3.6  N,  the  ionization  decreases 
with  increasing  temperature.  Those  solutions  for  which  m  is  less  than 
unity  exhibit  an  increase  in  ionization  throughout  with  decreasing  con- 
centration, while  those  solutions  for  which  m  is  greater  than  unity  exhibit 
first  a  decrease  and  then  an  increase,  so  that  the  ionization  curves  pass 
through  minima  in  the  neighborhood  of  0.1  N.  These  minima  are  the 
more  pronounced  the  greater  the  value  of  m.  In  very  dilute  solutions, 
again,  the  ionization  curves  approach  one  another,  corresponding  to  the 
fact  that  at  low  concentrations  the  ionization  in  all  cases  approaches  unity. 

18  Fitzgerald,  J.  Phya.  Chem.  16,  621   (1912). 


SOLUTIONS  AS  A  FUNCTION  OF  TEMPERATURE 
TABLE   LVIII. 


159 


CONDUCTANCE  OF  CONCENTRATED  SOLUTIONS  IN  METHYLAMINE  AND 

ETHYLAMINE. 


Salt 

AgNOg         

V 
0.2456 

Methylamine 
—  33.5° 
3.237 

—  15° 
6.180 

0° 
9.262 

+  15° 
13.05 

It 

0.4790 

14.33 

20.56 

25.67 

30.8 

n 

0.9348 

22.61 

28.92 

34.15 

38.77 

11 

2.084 

24.32 

29.48 

32.97 

34.95 

11 

5.449 

21.80 

25.18 

26.81 

27.41 

11 

10.63 

20.04 

22.19 

22.74 

22.19 

KI        

0.6094 

31.12 

38.17 

42.90 

46.49 

« 

1.190 

32.97 

38.52 

41.74 

43.96 

M 

2.320 

28.49 

31.45 

33.90 

33.39 

AgNO, 

0.4083 

Ethylamine. 
2.135 

3.989 

5.824 

8.072 

u 

0.7968 

5.310 

7.753 

10.09 

12.11 

tt 

0.9928 

5.67 

8.44 

10.55 

12.52 

u 

1.981 

5820 

7.625 

9082 

1025 

tl 

3.953 

4.320 

5.400 

6.141 

6.719 

(( 

7886 

2.683 

3.181 

3454 

3690 

tt 

15.73 

1.677 

1.818 

1.939 

1.939 

11 

3139 

1.212 

1.277 

1.285 

1  188 

LiCl  '  

0.4215 

1.586 

2.080 

n 

0.8224 

__ 

2.001 

2.447 

2.661 

ti 

1.604 

1.279 

1.763 

1.911 

1.835 

tt 

3.131 

0.8484 

0.9915 

0.976 

0.8052 

C2H6NH3C1  .... 
u 

n 
tt 
tt 
tt 

0.1666 
0.3253 
0.6346 
0.7676 
1.497 
2.922 

2.293 

3.692 
2.606 
1.285 

0.7197 
3.851 
5.090 
4.675 
2.921 
1.261 

1.450 
5.242 
5.820 
5.294 
2.992 
1.181 

2.440 
6.616 
6.406 
5.630 
2.886 
1.064 

If  the  values  of  the  ionization  given  by  the  lower  curves  in  the  figure 
are  multiplied  by  the  corresponding  A0  values,  the  conductance  curves 
shown  in  the  upper  part  of  the  figure  are  obtained.  At  low  concen- 
trations, where  the  ionization  decreases  only  little  with  rising  tempera- 
ture, the  increased  conductance,  due  to  temperature  rise,  more  than 
counterbalances  the  decreased  conductance  due  to  decreased  ionization, 
and  the  conductance  therefore  increases  with  increasing  temperature.  In 
very  concentrated  solutions,  also,  the  conductance  increases  with  the 
temperature  since  the  change  in  ionization  here  is  relatively  small.  At 


160        PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 


intermediate  concentrations,  however,  where  the  change  in  ionization  is 
large,  the  conductance-concentration  curves  at  different  temperatures 
intersect  one  another  in  a  more  or  less  complicated  manner,  indicating 
that  the  conductance-temperature  curves  in  this  region  exhibit  maxima. 


100 


100 


C  *.003| 


C«|.0 


50 


C..3J 


-50 


-JO  - 

Temperature. 


+  10 


FIG.  34.  Conductance-temperature  Curves,  illustrating  the  Relation  between  Con- 
ductance and  Temperature  for  Solutions  of  Electrolytes  at  Different  Concentra- 
tions in  Solvents  of  Relatively  Low  Dielectric  Constant. 

The  temperature- conductance  curves  are  shown  in  Figure  34  for  concen- 
trations from  1.0  to  0.001  normal.  At  0.001  normal  the  conductance 
increases  throughout  with  increasing  temperature.  As  the  temperature 
rises,  however,  the  conductance  change  due  to  a  given  temperature  change 
becomes  smaller  and  smaller  and  at  this  concentration  the  curve  is  very 
near  a  maximum  at  a  temperature  .of  +  10°.  At  a  concentration  of 
0.0031  normal,  the  conductance  curve  exhibits  a  very  flat  maximum  at  a 


SOLUTIONS  AS  A  FUNCTION  OF  TEMPERATURE  161 

temperature  of  — 10°.  As  the  concentration  of  the  solution  increases, 
the  maximum  is  shifted  toward  lower  temperatures  as  indicated  by  the 
dotted  curve.  At  0.01  normal  the  maximum  lies  in  the  neighborhood  of 
—  30°,  while  at  0.031  normal  the  maximum  is  still  further  displaced  in 
the  same  direction.  At  0.1  normal  the  maximum  remains  at  practically 
the  same  value,  but  at  0.31  normal  the  maximum  is  displaced  toward 
higher  temperatures,  being  very  flat  in  this  case  and  lying  somewhere 
in  the  neighborhood  of  — 10°.  At  1  normal  the  maximum  has  arisen  to 
temperatures  above  +  10°  and  the  conductance  increases  markedly  over 
the  entire  temperature  range  from  —  50°  to  +  10°  •  The  maximum 
occurs  at  the  lowest  temperature  at  a  concentration  in  the  neighborhood 
of  0.1  N.  These  curves  represent,  in  general,  the  behavior  of  solutions 
at  different  temperatures.  They  correspond  very  closely  with  the  values 
obtained  by  Franklin14  for  solutions  of  KI  in  S02.  The  maximum  in 
the  conductance-temperature  curves  shifts  from  higher  to  lower  tem- 
peratures with  increasing  concentrations,  reaches  a  minimum,  and  there- 
after again  shifts  from  lower  to  higher  temperatures  with  increasing  con- 
centration. In  certain  cases  the  effect  of  viscosity  is  such  that  it  just 
counterbalances  the  effect  of  increased  ionization  over  a  considerable 
temperature  interval.  Ammonium  sulphocyanate  dissolved  in  sulphur 
dioxide  is  an  example  of  this  type,  the  conductance  being  practically 
independent  of  temperature  at  a  concentration  of  approximately  0.1 
normal.  At  concentrations  greater  than  0.1  normal  the  temperature 
coefficient  of  ammonium  sulphocyanate  solutions  in  sulphur  dioxide  is 
positive  and  is  the  greater  the  greater  the  concentration  of  the  solution, 
while  at  lower  concentrations  the  temperature  coefficient  is  negative  and 
initially  increases  with  decreasing  concentration.  Ultimately,  however, 
the  sign  of  the  coefficient  must  change.  The  fact  that  solutions  in  all 
solvents,  without  exception,  exhibit  maxima  in  the  conductance-tempera- 
ture curves  at  intermediate  concentrations  indicates  that  at  the  tem- 
peratures in  question  the  constant  m  has  reached  a  value  near  or 
greater  than  unity.  Curves  of  this  type  have  been  observed  in  solu- 
tions in  ammonia,  sulphur  dioxide,  water,  methyl  and  ethyl  amine,  and 
methyl  and  ethyl  alcohols.  It  is  not  to  be  doubted  that  the  phenomenon 
is  a  general  one.  That  the  temperature  coefficient  of  solutions  becomes 
positive  at  very  high  concentrations  is  indicated  by  practically  all  data 
available  for  solutions  at  high  concentrations.  In  general,  it  has  been 
found  that  the  higher  the  concentration  the  greater  the  value  of  the  tem- 
perature coefficient,  or  rather  that  the  temperature  coefficient  passes 
through  a  minimum  or  negative  value  at  intermediate  concentrations. 

"  Franklin,  loc.  cit. 


162        PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 


This  result,  however,  does  not  become  apparent  in  solutions  of  high 
dielectric  constant,  since  the  effects  in  question  become  marked  only 
when  the  constant  ra  approaches  a  value  of  unity  or  greater. 

With  increasing  concentration,  the  temperature  of  the  conductance 
maximum  decreases,  passes  through  a  minimum  and  thereafter  again 
increases  in  the  more  concentrated  solutions.  This  course  of  the  curve 


V  =  16.3 

V  *  8-14 
V-S.I7 


20° 

Temperature. 


+0* 


FIG.  35.    Showing  the  Conductance  as  a  Function  of  the  Temperature  for  Solutions 
of  Cobalt  Chloride  in  Ethyl  Alcohol  at  Different  Concentrations. 

is  illustrated  in  Figure  35,  in  which  are  plotted  the  temperature-con- 
ductance curves  for  cobalt  chloride,  CoCl2,  in  ethyl  alcohol.15  The 
course  of  the  maximum  is  here  indicated  by  the  broken  line.  The  lowest 
point  of  the  maximum  temperature  is  approximately  31°  and  at  a 

an<J  Weitzel,  Ztschr.  /.  phys.  Chem.  79,  279  (191?) , 


SOLUTIONS  AS  A  FUNCTION  OF  TEMPERATURE 


163 


of  approximately  50  liters.  At  higher  concentrations  the  maximum  tem- 
perature increases  very  rapidly,  while  at  lower  concentrations  the  maxi- 
mum increases  more  slowly.  In  solvents  of  lower  dielectric  constant, 
the  curve  of  maxima  proceeds  to  lower  temperatures.  In  Figure  36  are 
shown  curves  for  cobalt  chloride  in  acetone.16  In  this  case  the  branch 


! 


V;6-' 


Temperature. 

FIG.  36.    Showing  the  Conductance  as  a  Function  of  the  Temperature  for  Solutions 
of  Cobalt  Chloride  in  Acetone  at  Different  Concentrations. 

of  the  maximum  at  lower  concentrations  lies  at  very  low  values  of  the 
concentration  and  does  not  appear  on  the  figure.  At  higher  concentra- 
tions the  course  of  the  maximum  temperature  is  indicated  by  the  broken 
line.  At  all  points  to  the  right  of  the  maximum  curve  the  temperature 
coefficients  of  the  solution  are  negative.  In  Figure  37  are  shown  the 
conductance  temperature  curves  for  potassium  iodide  in  methylamine,  the 
dot'ted  curves  relating  to  dilutions  greater  than  28.2  liters.17  The  relation 

"Rimbach  and  Weitzel,  loc.  cif. 
*T  Fitzgerald,  loc.  cit. 


164        PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

among  the  curves  in  this  case  appears  quite  complex,  since  at  the  highest 
concentrations  the  conductance  decreases  with  increasing  concentration. 


-15° 

Temperature. 

FIG.  37.    Representing  the  Conductance  as  a  Function  of  the  Temperature  for  Solu- 
tions of  Potassium  Iodide  in  Methylamine  at  Different  Concentrations. 

The  course  of  the  maximum  temperatures  is  indicated  by  the  broken 
lines  which  meet  at  a  point  at  a  temperature  of  —  33°  and  at  a  dilution 
of  28.2  liters.  At  higher  concentrations  the  maximum  proceeds  to  higher 
temperatures  quite  rapidly,  while  at  lower  concentrations  the  temperature 


SOLUTIONS  AS  A  FUNCTION  OF  TEMPERATURE  165 

of  the  maximum  increases  slowly.    Similar  curves  have  been  found  for 
solutions  in  ethylamine,  methylamine,  and  sulphur  dioxide. 

While  the  complete  conductance-temperature  diagram  is  not  known 
for  most  solvents,  sufficient  data  exist  to  indicate  that  it  is  a  general 
property  of  electrolytic  solutions  to  exhibit  an  increasing  positive  tem- 
perature coefficient  at  high  concentrations.  In  certain  cases  this  coeffi- 
cient may  be  very  great.  In  other  cases  the  coefficient  at  lower  concen- 
trations is  negative,  decreasing  with  the  concentration  and  becoming 
positive  at  higher  concentrations.  In  the  following  table  is  given  a  list 
of  temperature  coefficients  for  substances  dissolved  in  the  liquid  halogen 
acids.18  The  coefficients  are  positive  unless  otherwise  indicated. 

TABLE  LIX. 

TEMPERATURE  COEFFICIENT  a  X  100  OF  SOLUTIONS  OF  ELECTROLYTES  IN 

DIFFERENT  SOLVENTS. 

Hydrogen  Bromide. 

Electrolyte  Vx          a±           V2  a,  V,           a, 

Acetic  Acid 4.30      2.62  0.571  2.72 

Butyric  Acid   4.18      2.68  0.817  3.70 

Iso-valeric  Acid  4.37      2.45  0.729  3.96 

Benzoic  Acid  8.82      0.53  2.38  0.72      1.14        0.89 

Metatoluic  Acid 5.85      0.15  1.83  0.93 

Hydroxybenzoic  Acid  . . .  18.4        1.00  1.36  2.15 

Methyl  Alcohol 1.75      2.5  1.25  4.2 

Metacresol 15.0  —  7.71  1.00  +  1.16 

Thymol  43.6          .47  7.34  0.00 

Alphanaphthol 51.6        2.26  18.0  0.30 

Hydrogen  Chloride. 

Propionic  Acid  11.8        2.15  2.5  2.91 

Butyric  Acid 50.1        2.80  0.792  3.27 

Methyl  Alcohol 2.91       1.21  1.06  2.68 

Ethyl  Alcohol 4.66      3.9  0.591  4.0 

Butyl  Alcohol 5.07      5.23  0.574  6.5 

Resorcin    137.0   —1.33  6.29  0.00      0.539     +1.3 

With  the  exception  of  solutions  of  thymol  and  alphanaphthol  in 
liquid  hydrogen  bromide,  the  positive  temperature  coefficients  through- 
out increase  with  increasing  concentration.  For  lack  of  more  compre- 
hensive experimental  data  regarding  the  temperature  coefficient  of  the 
substances  named,  it  is  impossible  to  hazard  a  guess  as  to  the  reason  for 
the  decrease  of  the  positive  temperature  coefficients  in  the  case  of  the 
solutions  of  these  two  substances.  Particularly  notable  is  the  high  nega- 

«  Archibald,  Journal  de  Chimie  Physique  11,  741   (1913). 


166        PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

tive  temperature  coefficient  of  the  solution  of  metacresol  in  liquid  hydro- 
gen bromide  at  a  dilution  of  15  liters.  Evidently,  the  temperature 
coefficient  in  this  case  changes  greatly  with  the  concentration  since  at 
normal  concentration  the  coefficient  is  positive  and  equal  to  1.16  per  cent. 

It  is  difficult  to  account  for  the  large  value  of  the  positive  tempera- 
ture coefficients  of  the  very  concentrated  solutions,  except  on  the  assump- 
tion that  the  ionization  in  the  case  of  these  solutions  is  relatively  inde- 
pendent of  the  temperature.  While  the  concentration  at  which  this  con- 
dition is  fulfilled  varies  considerably  with  the  nature  of  the  dissolved 
electrolyte,  it  varies  but  little  with  the  nature  of  the  solvent.  While  at 
lower  concentrations  the  ionization  decreases  throughout  with  the  tem- 
perature, at  higher  concentrations  the  ionization  increases  with  the 
temperature. 

It  is  probable  that,  at  very  low  concentrations,  the  temperature 
coefficient  will  always  be  found  positive.  The  concentration  at  which 
this  holds,  however,  may  be  very  low  indeed  in  the  case  of  solvents  of 
very  low  dielectric  constant.  It  may  be  noted,  in  this  connection,  that 
the  conductance-temperature  coefficient  of  nearly  all  solvents  is  positive. 
It  is  true  that,  if  no  impurities  were  present,  it  might  be  expected  that 
the  ionization  of  the  solvent  would  increase  with  the  temperature.  How- 
ever, in  most  cases,  the  final  conductance  of  highly  purified  solvents  is 
due  to  impurities  and  not  to  the  ionization  of  the  pure  solvent.  What- 
ever these  impurities  may  be,  it  is  evident  that  they  must  be  sufficiently 
ionized  at  these  concentrations  to  yield  a  positive  conductance-tempera- 
ture coefficient. 

The  ionization  as  a  function  of  the  concentration  at  different  tem- 
peratures is  represented  by  a  family  of  curves  passing  through  two  com- 
mon points  at  a  concentration  zero,  where  the  ionization  is  unity,  and  at 

a  concentration  corresponding  to  the  ionization  Y— "i ™  which  for 

solutions  of  potassium  iodide  in  sulphur  dioxide  is  in  the  neighborhood 
of  3.5  normal.  At  concentrations  below  this  value  the  ionization  de- 
creases with  the  temperature.  In  very  concentrated  and  very  dilute 
solutions,  the  decrease  in  the  ionization  is  comparatively  small,  and  the 
conductance  therefore  increases  with  the  temperature.  At  intermediate 
concentrations,  the  conductance  at  higher  temperatures  decreases  with 
the  temperature,  while  at  low  temperatures  it  increases  with  the  tempera- 
ture. If  the  A,  T-curves  are  examined,  it  will  be  found  that  at  inter- 
mediate concentrations  the  conductance  curves  exhibit  a  maximum.  As 
the  concentration  decreases,  however,  this  maximum  is  displaced  toward 
higher  temperatures  and  presumably  would  ultimately  disappear  at  suf- 


SOLUTIONS  AS  A  FUNCTION  OF  TEMPERATURE  167 

ficiently  low  concentrations.  It  is  to  be  borne  in  mind,  however,  that  at 
very  high  temperatures  the  value  of  the  mass-action  constant  becomes 
extremely  low,  as  may  be  seen  from  the  value  of  this  constant  in  the  case 
of  solvents  having  low  dielectric  constants.  It  is  possible,  therefore, 
that,  in  the  case  of  solvents  having  relatively  low  dielectric  constants,  the 
mass-action  constant  has  such  a  low  value  that  a  maximum  in  the  con- 
ductance curves  will  not  be  observed  in  dilute  solutions.  At  higher  con- 
centrations, again,  the  maximum  is  displaced  toward  higher  temperatures 
and  if  it  were  possible  to  work  with  solutions  of  sufficiently  high  concen- 
trations the  maximum  should  disappear  entirely.  Data  are  not  available 
in  this  case  at  temperatures  approaching  the  critical  point,  but,  in  solu- 
tions in  sulphur  dioxide  and  ethyl  amine,  the  conductivity  increases  with 
the  temperature  over  those  ranges  of  temperature  for  which  conductance 
data  exist. 

The  conductance  of  a  given  solution,  therefore,  appears  to  be  a  func- 
tion, primarily,  of  the  fluidity  of  the  medium  and  of  its  dielectric  con- 
stant. For  a  given  type  of  salt  the  conductance  curve  in  twp  solvents  at 
different  temperatures  will  be  similar,  provided  that  the  two  solvents 
have  the  same  value  of  the  dielectric  constant. 

4.  The  Conductance  of  Solutions  in  the  Neighborhood  of  the  Critical 
PoinL  Data  relative  to  the  ionization  of  solutions  in  the  critical  region 
are  entirely  lacking,  for  which  reason  it  is  not  possible  to  interpret  the 
results  of  conductance  measurements  with  any  degree  of  certainty.  How- 
ever, the  conductance  data  indicate  that  the  properties  of  solutions  in 
the  critical  region  do  not  differ  materially  from  those  of  solutions  at  lower 
temperatures.  Moreover,  it  appears  that  the  property  of  forming  elec- 
trolytic solutions  is  by  no  means  confined  to  the  liquid  state  of  matter. 
Fluids  above  the  critical  point  yield  electrolytic  solutions  and  even  the 
solvent  vapors  themselves,  below  the  critical  point,  possess  the  power  of 
dissolving  electrolytes,  forming  solutions  which  conduct  the  current. 

It  has  already  been  pointed  out  that,  as  the  critical  point  is  ap- 
proached, the  conductance  of  solutions  in  solvents  of  low  dielectric  con- 
stant approaches  a  very  low  value,  and  that  the  conductance-temperature 
curve  if  extrapolated  would  intersect  the  temperature  axis  at  a  tem- 
perature not  far  removed  from  the  critical  temperature.  It  is  known, 
however,  that,  once  the  critical  point  has  been  reached,  the  conductance 
falls  only  very  slowly  with  increasing  temperature.  It  other  words,  the 
conductance-temperature  curves  exhibit  a  discontinuity  in  the  immediate 
neighborhood  of  the  critical  point.  As  will  be  seen  below,  this  behavior 
is  what  we  should  expect  when  conductance  measurements  are  carried 
out  in  sealed  tubes,  where  the  total  volume  of  liquid  and  vapor  remains 


168        PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

constant.  In  the  immediate  neighborhood  of  the  critical  point,  the 
density  of  the  solvent  decreases  very  rapidly  with  increasing  temperature, 
whereas  beyond  the  critical  region  the  density  of  the  solvent  medium 
remains  fixed.  The  rapid  decrease  in  conductance  immediately  below 
the  critical  point  is  to  be  ascribed  to  the  rapid  decrease  in  the  density  of 
the  solvent  medium. 

It  is  to  be  expected  that  the  ionization  and  consequently  the  con- 
ductance of  solutions  in  the  critical  region  will  be  governed  largely  by 
the  dielectric  constant  of  the  medium,  and  it  may  be  inferred  that  those 
liquids,  which  under  ordinary  conditions  exhibit  a  very  high  dielectric 
constant,  will  likewise  exhibit  a  relatively  high  dielectric  constant  in  the 
critical  region.  In  the  case  of  sulphur  dioxide  and  ammonia  the  dielec- 
tric constant  in  the  critical  region  is  very  low,  whereas  in  the  case  of  the 
lower  alcohols  and  water  a  relatively  larger  value  of  this  constant  is  to 
be  expected.  Water  would  be  an  ideal  substance  for  the  purpose  of 
studying  the  properties  of  electrolytic  solutions  in  the  critical  region, 
were  it  not  for  the  difficulties  attending  conductance  measurements  in 
this  solvent  at  high  temperatures.  These  difficulties,  however,  disappear 
very  largely  in  the  case  of  the  lower  alcohols,  although  it  is  to  be  ex- 
pected that  the  ionization  in  the  critical  region  will  be  markedly  lower 
in  these  solvents  than  in  water. 

In  Table  LX  are  given  values  of  the  specific  conductance  of  solutions 
of  potassium  iodide  in  methyl  alcohol  at  a  series  of  temperatures  up  to 
252°.19  The  critical  point  lies  in  the  neighborhood  of  240°  C.  The 
reduced  conductance  values  given  in  the  last  column  are  derived  by 
multiplying  the  specific  conductance  (second  column)  by  the  fraction 
of  the  total  volume  of  the  tube  occupied  by  the  liquid  (third  column). 
If  the  true  critical  phenomenon  is  to  be  observed,  the  tube  must  initially 
be  filled  with  an  amount  of  liquid  such  that  when  the  critical  point  is 
reached  the  tube  is  just  filled  with  liquid.  Obviously,  as  the  liquid 
expands,  the  concentration  of  the  solution  decreases,  and  the  corrected 
values  of  the  specific  conductance  therefore  represent  values  of  this 
quantity  on  the  assumption  that  the  specific  conductance  varies  as  a 
linear  function  of  the  concentration.  This  condition  is  probably  not 
fulfilled,  but  nevertheless  represents  an  approximation  somewhat  nearer 
the  truth  than  the  measured  values  of  the  specific  conductance.  More- 
over, in  the  immediate  neighborhood  of  the  critical  region,  where  the 
volume  of  the  liquid  is  almost  equal  to  the  entire  volume  of  the  tube,  the 
corrected  value  of  the  specific  conductance  corresponds  very  nearly  with 
the  true  value.  If  these  corrected  values  are  plotted  against  the  tem- 

"Kraus,  Pfy/8.  Rev.  18,  40  and  89  (1904). 


SOLUTIONS  AS  A  FUNCTION  OF  TEMPERATURE 


169 


perature,  then  a  break  in  the  conductance  curve  itself  will  not  occur  at 
the  critical  point.    The  results  are  shown  graphically  in  Figure  38. 

TABLE  LX. 

SPECIFIC  CONDUCTANCE  OF  KI  IN  CH3OH  THROUGH  THE 
CRITICAL  REGION,  AT  3.34  X  10'*  N. 


Liquid. 


90.0 
102.0 
123.0 
138.2 
149.0 
159.0 
171.0 
183.8 
197.0 
208.5 
220.0 
225.0 
230.0 
237.0 
238.0 
238.5 
239.0 
239.5 
240.04 
240.4 
240.5 
240.6 
Grit. 


t 

240.7 
240.8 
240.9 
241.0 
241.2 
241.4 
241.6 
241.92 


908.4 
1006.0 
1098.0 
1126.0 
1139.0 
1126.0 
1076.0 
1006.0 
740.4 
617.0 
431.2 
337.5 
252.1 
186.0 
157.6 
143.7 
127.0 
107.5 
83.71 
63.92 
55.46 
45.29 
42.65 


Gas. 


nxio6 

42.14 
41.56 
40.98 
40.41 
39.52 
38.68 
37.89 
37.06 


V  /V 

0.4324 
.4363 
.4451 
.4548 
.4674 
.4764 
.4853 
.4979 
.5095 
.5137 
.5445 
.5569 
.5693 
.6005 
.6094 
.6183 
.6275 
.6362 
.6628 
.7432 
.8074 
.9566 

1.000 


t 

242.45 

243.4 

244.4 

245.46 

247.1 

249.1 

252.0 


V  /V  X  10' 

392.8 
438.9 
488.2 
511.9 
532.3 
536.2 
522.5 
500.9 
377.3 
314.3 
234.8 
187.9 
143.5 
111.6 

96.05 

88.88 

79.69 

68.39 

55.50 

47.50 

44.78 

43.32 

42.65 


HX106 
36.10 
34.45 
32.88 
31.24 
29.11 
26.59 
23.92 


It  will  be  observed  that  the  conductance  passes  through  a  maximum 
somewhere  between  159°  and  197°,  probably  not  far  from  175°.  There- 
after the  conductance  decreases  rapidly,  particularly  in  the  immediate 


170        PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 


neighborhood  of  the  critical  point,  which  in  this  case  is  240.6°.  At  the 
critical  point  the  rapid  decrease  in  conductance  with  the  temperature 
ceases  abruptly  and  thereafter  there  is  only  a  moderate  decrease  as  the 
temperature  increases.  Between  239.5°  and  240.6°  there  is  a  conduct- 
ance decrease  of  approximately  50  per  cent  for  a  temperature  change  of 
1°,  whereas  between  240.6°  and  252°  there  is  a  decrease  of  less  than 
50  per  cent  for  a  temperature  change  of  approximately  12°.  The  sharp 
break  in  the  tangent  to  the  curve  at  the  critical  point  is  very  noticeable. 


800 


400 


ZOO 


SZO*  140*  I&O*  IRQ*  ZOO*  ZSO*  £+0* 

Temperature. 

FIG.  38.    Representing  the  Conductance  of  Solutions  of  Potassium  Iodide  in  Methyl 
Alcohol  as  a  Function  of  the  Temperature  through  the  Critical  Region. 

This  result  is  obviously  due  to  the  fact  that  below  the  critical  temperature 
the  observed  conductance  change  is  due  to  the  combined  effect  of  tem- 
perature and  of  density  change,  while  above  the  critical  point  it  is  due 
to  temperature  change  alone. 

As  the  critical  point  is  approached,  the  salt  becomes  appreciably 
soluble  in  the  vapor  and  is  sufficiently  ionized  to  render  the  vapor  a 
fairly  good  conductor.  In  Table  LXI,  are  given  values  of  the  specific 
conductance  of  liquid  and  vapor  for  solutions  of  ammonium  chloride  in 
methyl  alcohol,  together  with  the  relative  volume  of  the  liquid 

V. 

phase  -jf. 


SOLUTIONS  AS  A  FUNCTION  OF  TEMPERATURE  171 

In  this  solution  the  amount  of  liquid  in  the  tube  was  such  that  its 
mean  density  was  below  the  critical  density.  In  such  case  the  true 
critical  phenomenon  does  not  occur  since,  if  carried  out  under  strictly 
equilibrium  conditions,  the  liquid  disappears  at  the  bottom  of  the  tube. 
In  general,  however,  unless  the  amount  of  liquid  is  comparatively  small, 

TABLE  LXI. 

CONDUCTANCE  OF  0.2245  PER  CENT   NH4C1  IN  CH3OH  IN  THE 
CRITICAL  REGION. 

Temp.  \i  Liquid  u  Vapor  V  t/V 

234.0  1524.0  .4411 

236.9  1236.0  1.574  .4333 

239.0  930.3  2.177  .4261 

240.0  760.0  3.568  .4147 

241.0  605.7  6.381  .4000 
241.9  469.7  14.64  .3707 
242.5  257.7  38.66  .2806 

-*  Crit.  Pt. 

243.1  67.25 

245.2  54.36 
247.1  47.62 
249.0  41.33 
254.0  30.19 

and  is  thoroughly  stirred,  it  will  be  found  that  the  meniscus  fades  away 
at  some  point  above  the  bottom  of  the  tube  at  a  temperature  correspond- 
ing to  the  critical  temperature.  At  this  temperature,  the  specific  con- 
ductance of  the  vapor  phase  was  approximately  one  sixth  that  of  the 
liquid  phase.  The  conductance  of  the  vapor  phase  is  readily  appreciable 
as  much  as  5°  below  the  critical  point.  Above  the  critical  point  the 
conductance  of  the  solution  in  a  gas  below  its  critical  density  decreases 
with  the  temperature,  the  decrease  amounting  to  something  over  50  per 
cent  for  a  temperature  change  of  approximately  12°.  In  the  immediate 
neighborhood  of  the  critical  point  the  conductance  appears  to  change 
somewhat  more  rapidly  than  at  higher  temperatures. 

The  conductance  of  the  vapor  phase  increases  very  rapidly  with  the 
temperature,  and  the  more  rapidly  the  nearer  the  temperature  lies  to  the 
critical  point.  It  is  evident  that  several  factors  are  here  coming  into 
play.  In  the  first  place,  the  concentration  of  the  salt  in  the  vapor  phase 
increases  with  rising  temperature;  and,  in  the  second  place,  the  density 
of  the  vapor  increases  with  increasing  temperature.  As  follows  from 
the  results  given  below  for  the  conductance  of  the  fluid  phase  above  the 
critical  temperature  as  a  function  of  the  concentration  of  the  solvent,  the 


172        PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 


conductance  increases  very  rapidly  with  increasing  density  of  the  solvent 
phase.  As  the  density  of  the  vapor  increases  as  the  critical  point  is 
approached,  the  conductance  is  increased  very  largely  because  of  the 
increase  in  the  density  of  the  vapor.  The  relations  between  the  curves 
are  shown  in  Figure  39. 

In  the  following  table  are  given  values  of  the  specific  conductance 
of  a  0.00463  normal  solution  of  potassium  iodide  in  methyl  alcohol  for 
different  concentrations  of  the  solvent.20 

TABLE  LXII. 

CONDUCTANCE  OF  POTASSIUM  IODIDE  IN  METHYL  ALCOHOL  ABOVE  THE 
CRITICAL  POINT  FOR  DIFFERENT  DENSITIES  OF  SOLVENT. 

0  =  0.1188%       V  —  0.3981         17  =  0.1163        C  —  0.00463  N 

HX106 
t  W=  0.1163     0.1023        0.0968        0.0815 


__  42.24  — 


0.0758        0.0588 
—  1.892 

1.736 
—  4.783  — 


239.0 

241.0 

241.3 

241.32 

241.5 

241.6 

241.7 

242.0 

242.9 

243.0 

244.0 

244.9 

245.0 

245.1 

247.0 

247.2 

250.1 


In  this  table  W  represents  the  weight  of  solvent  in  the  tube,  V  the 
total  volume  of  the  tube  in  cubic  centimeters  and  C  the  concentration  of 
the  solution.  The  conductance  curves  are  shown  graphically  in  Figure 
40.  The  density  of  the  solvent  in  the  different  experiments,  together  with 
he  conductance  of  the  solutions  at  245°  and  250°,  is  given  in  Table 
LXIII.  (See  page  174.) 

It  is  evident  that  the  conductance  of  a  solution  containing  a  given 
amount  of  salt  and  a  variable  amount  of  solvent  increases  enormously 
as  the  density  of  the  solvent  increases.  For  an  increase  in  the  density 
of  the  methyl  alcohol  from  0.127  to  0.251,  the  conductance  increases 

*°  Kraus,  loc.  cit. 


56.41 

— 

28.80 

— 

— 

— 

— 

— 

— 

16.56 

— 

— 

53.95 

36.35 

26.54 

10.90 

4.468 

— 

— 

— 

— 

— 

— 

1.662 

50.54 

32.48 

24.23 

9.36 

4.141 



47.90 

30.59 

22.47 

8.626 

3.884 

— 

— 

— 

— 

— 

— 

1.521 

— 

28.80 

21.25 

7.886 

3.656 

— 

45.51 

— 

— 

— 

— 



41.68 

25.79 

19.14 

7.081 

3.247 



— 

— 

— 

— 

— 

1.387 

36.97 

22.04 

16.90 

6.003 

2.824 

1.230 

SOLUTIONS  AS  A  FUNCTION  OF  TEMPERATURE 
600 

500 


173 


>  400 


1300 


200 


IOO 


00 


Temperature  °C. 


FIG.  39.     Representing  the  Conductance  of  Ammonium  Chloride  in  Methyl  Alcohol 
as  a  Function  of  the  Temperature  in  the  Critical  Region. 


60 


50 


40 


30 


237 


239 


241 


243  245 

TEMPERATURES 


247 


249 


251 


FIG.  40.    Representing  the  Cpnductance  of  Potassium  Iodide  in  Methyl  Alcohol 
above  the  Critical  Point  at  Various  Concentrations  of  the  Solvent. 


174        PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

TABLE   LXIII. 

CONDUCTANCE  OF  KI  IN  CH3OH  AS  A  FUNCTION  OF  THE  DENSITY 
OF  THE  SOLVENT. 

Density  \i  X  106 

of  Solvent  245°  250° 

0.251  45.6  37.2 

0.220  28.8  22.6 

0.208  21.2                  .  16.83 

0.178  8.0  6.0 

0.163  3.7  2.8 

0.127  1.44  1.2 

from  1.44  to  45.6,  or  approximately  50  times.  At  250°  the  increase  in 
the  conductance  is  not  so  great,  since  for  the  same  concentration  change 
the  conductance  increases  only  from  1.2  to  37.2,  or  30  times.  The 
A,  ^-curves  indicate  a  fairly  rapid  decrease  in  the  conductance  immedi- 
ately above  the  critical  temperature.  As  the  temperature  rises  these 
curves  appear  to  approach  a  horizontal  straight  line.  The  lower  the 
concentration,  the  less  does  the  conductance  change  with  the  temperature. 

At  a  given  temperature,  the  addition  of  a  given  amount  of  solvent 
increases  the  conductance  the  more  the  greater  the  density  of  the  solvent. 
In  other  words,  the  A,C-curves  at  constant  temperature  are  strongly 
convex  toward  the  axis  of  concentrations. 

It  is  to  be  borne  in  mind  that  the  conductance  of  a  solution  is  a 
function  of  the  number  of  carriers  and  the  speed  with  which  these  car- 
riers move.  Unless  the  nature  of  the  carriers  changes  very  greatly,  we 
should  expect  that  the  speed  of  the  carriers  would  be  the  greater  the 
lower  the  density  of  the  solvent,  since  the  viscosity  of  a  gas  increases 
with  its  density.  Since,  now,  the  conductance  of  a  solution  increases 
very  rapidly  with  the  density  and  since  this  increase  is  the  greater  the 
greater  the  density  of  the  solvent,  it  is  difficult  to  escape  the  conclusion 
that  the  increase  in  the  conductance  of  these  solutions  is  due  to  an 
increase  in  the  number  of  carriers  present  in  them. 

According  to  the  commonly  accepted  theory  of  electrolytic  solutions, 
the  change  in  the  conductance  of  solutions  as  a  function  of  the  concen- 
tration is  due  to  a  change  in  the  relative  number  of  carriers;  that  is, 
to  a  change  in  the  ionization  of  the  electrolyte.  Because  of  various 
difficulties  which  have  arisen  in  accounting  for  the  properties  of  strong 
electrolytes,  some  writers  have  suggested  that  strong  electrolytes  in 
solution  are  completely  ionized.  The  study  of  the  properties  of  non- 
aqueous  solutions  and  of  solutions  at  higher  temperatures  yields  no 
apparent  support  for  such  an  hypothesis.  If  the  salts  in  solvents  of  low 


SOLUTIONS  AS  A  FUNCTION  OF  TEMPERATURE  175 

dielectric  constant  are  completely  ionized,  then  it  becomes  exceedingly 
difficult  to  account,  on  the  one  hand,  for  the  very  low  value  of  the  con- 
ductance of  these  solutions  at  certain  intermediate  and  low  concentra- 
tions and,  on  the  other  hand,  for  the  very  rapid  increase  in  the  conduct- 
ance of  these  solutions  at  higher  concentrations.  So,  in  the  case  of 
solutions  in  the  neighborhood  of  the  critical  point,  it  is  difficult  to  account 
for  the  rapid  decrease  in  the  conductance  of  the  solution  as  the  critical 
point  is  approached  on  the  basis  of  this  hypothesis.  Again,  in  the  case 
of  solutions  above  the  critical  point,  the  large  increase  in  the  conductance 
of  the  solution  as  the  concentration  of  the  solvent  increases  is  with  diffi- 
culty accounted  for  on  the  assumption  that  the  electrolyte  is  completely 
ionized,  unless,  at  the  same  time,  an  hypothesis  is  introduced  according 
to  which  the  speed  of  the  ions  through  the  solvent  medium  is  enormously 
increased  by  an  increase  in  the  concentration  of  the  solvent.  For  such 
an  hypothesis  there  is  an  entire  lack  both  of  experimental  facts  and  of 
theoretical  support. 

On  the  other  hand,  if  the  fundamental  elements  of  the  usual  theory 
of  electrolytes  are  accepted,  we  are  forced  to  the  conclusion  that  the  ion- 
ization  of  electrolytes  is  a  complex  function  of  the  concentration  and  that, 
at  very  high  concentrations,  in  the  case  of  solvents  of  low  dielectric  con- 
stant, the  ionization  increases  with  the  concentration.  While  theoretical 
support  is  lacking  for  this  assumption,  no  theoretical  principle's  are  con- 
tradicted by  such  an  hypothesis.  Furthermore,  if  we  assume  that  the 
ionization  of  electrolytes  is  a  function  of  the  concentration  and  is  approxi- 
mately measured  by  the  conductance  ratio  -T-,  the  influence  of  tempera- 

A0 

ture,  of  concentration,  and  of  the  viscosity  of  the  solvent  may  be  readily 
accounted  for  without  contradicting  known  facts  and  without  intro- 
ducing any  further  hypotheses  for  which  a  theoretical  foundation  is 
lacking.  In  other  words,  on  the  basis  of  the  ionization  hypothesis,  it  is 
necessary  to  make  only  a  single  assumption  whose  correctness  remains 
uncertain,  whereas  in  the  case  of  other  hypotheses  a  number  of  assump- 
tions are  necessary.  Unless  other  and  more  conclusive  facts  can  be 
adduced  in  support  of  the  hypothesis  that  the  strong  electrolytes  are 
completely  ionized  in  solution,  this  hypothesis  is  clearly  untenable  at 
the  present  time. 


Chapter  VII. 
The  Conductance  of  Electrolytes  in  Mixed  Solvents. 

1.  Factors  Governing  the  Conductance  of  Electrolytes  in  Mixed 
Solvents.  Since  the  properties  of  electrolytic  solutions  are  functions  of 
the  properties  of  the  solvent,  it  follows  that  in  the  case  of  mixed  solvents 
the  properties  will  be  functions  of  the  concentration  of  the  solvents  in  the 
mixture.  We  may  have  mixtures  in  which  either  one  or  both  of  the 
solvents  are  capable  of  forming  electrolytic  solutions  with  ordinary  salts. 
In  the  case  of  water,  mixtures  are,  as  a  rule,  obtained  only  with  other 
solvents  which  have  the  power  of  forming  electrolytic  solutions.  In  the 
case  of  certain  non-aqueous  solvents,  however,  mixtures  may  be  obtained 
with  solvents  not  capable  of  forming  electrolytic  solutions  with  ordi- 
nary salts. 

The  addition  of  a  second  solvent  component  to  a  solution  of  given 
concentration  will  in  general  affect  the  conductance  in  that  the  speed 
of  the  ions  and  the  ionization  of  the  electrolyte  will  be  influenced  by  the 
addition  of  the  second  solvent.  The  conductance  will  therefore  be  a 
more  or  less  complex  function  of  the  relative  concentration  of  the  two 
solvents.  The  effect  of  the  addition  of  a  second  solvent  will  depend 
upon  the  concentration  of  the  electrolyte  as  well  as  upon  its  nature. 

In  certain  solutions,  the  formation  of  an  electrolytic  solution  depends 
upon  an  interaction  between  the  dissolved  substance  and  the  solvent. 
When  such  is  the  case,  the  conductance  of  the  solution  is  often  greatly 
affected  by  the  addition  of  a  second  solvent  component.  Such  is  the  case 
with  solutions  of  the  acids  in  non-aqueous  solvents  on  the  addition  of 
water.  The  addition  of  a  small  amount  of  water  to  a  solution  of  an 
acid  in  an  alcohol,  for  example,  has  an  enormous  influence  upon  the 
properties  of  the  resulting  solution.  Similar  results  are  obtained  in  non- 
aqueous  solutions  of  salts  which  exhibit  a  pronounced  tendency  to  form 
hydrates,  as,  for  example,  calcium  chloride. 

If  we  assume  that  the  nature  of  the  ions  remains  fixed  and  inde- 
pendent of  the  nature  of  the  second  solvent,  then  we  should  expect  the 
speed  of  the  ions  to  be  a  function  of  the  viscosity  of  the  medium.  The 
viscosity  of  a  mixture  of  two  solvents  varies  continuously  with  the  rela- 
tive concentration  of  the  solvents.  The  viscosity  curves  may  exhibit 
either  a  minimum  or  a  maximum  or  they  may  vary  continuously  between 

176 


ELECTROLYTES  IN  MIXED  SOLVENTS  177 

the  values  of  the  two  pure  media  as  extremes.  If  the  viscosity  of  the  two 
solvents  differs  greatly,  then  in  general  the  viscosity  of  a  mixture  will  lie 
intermediate  between  that  of  the  two  pure  components.  If  the  two  sol- 
vents have  approximately  the  same  viscosity  and  particularly  if  both 
solvents  are  associated  liquids,  the  viscosity  curve  will  as  a  rule  exhibit 
a  maximum.  Cases  in  which  the  viscosity  curve  passes  through  a  mini- 
mum are  rather  exceptional. 

The  viscosity  of  a  mixture  of  two  solvents  will  in  all  cases  be  of  the 
same  order  of  magnitude  as  that  of  the  two  components.  If  the  nature 
of  the  ions  remains  fixed,  therefore,  the  speed  of  the  ions  may  be  ex- 
pected to  vary  approximately  in  proportion  to  the  fluidity  change. 

In  adding  a  second  solvent  to  a  solution  of  an  electrolyte  in  another 
solvent,  an  interaction  may  take  place  between  the  electrolyte  and  the 
added  solvent.  In  this  case,  the  nature  of  the  ions  will  change  and  with 
it,  in  general,  their  speed.  In  some  instances,  the  change  in  the  speed 
of  the  ions  due  to  this  cause  is  relatively  large. 

In  general,  it  may  be  expected  that  the  ionization  of  a  salt  in  a  mixture 
of  two  solvents,  particularly  in  dilute  solutions,  will  have  a  value  inter- 
mediate between  those  of  the  same  electrolyte  in  the  pure  solvents.  For 
we  have  seen  that  the  ionization  of  a  salt  is  a  function  of  the  dielectric 
constant  of  the  medium,  and  the  dielectric  constant  of  a  mixture  of  two 
solvents  is  in  general  intermediate  between  those  of  the  pure  components. 
Here  again,  however,  we  have  to  take  into  account  the  interaction  between 
the  electrolyte  and  the  components  which  form  the  solvent  medium.  If 
interaction  takes  place  between  the  second  solvent  and  the  electrolyte, 
then  a  new  complex  is  formed  whose  ionization  may  differ  greatly  from 
that  of  the  same  electrolyte  in  the  first  solvent  and,  in  fact,  all  of  whose 
chemical  properties  may  differ  greatly  from  those  of  the  original  electro- 
lyte in  the  first  solvent.  A  considerable  number  of  examples  of  this  type 
are  found  in  aqueous  solutions.  When,  for  example,  ammonia  is  added 
to  a  solution  of  a  silver  salt  in  water,  a  complex  is  formed  between  the 
silver  ion  and  ammonia,  which  apparently  has  the  composition 
Ag(NH3)2+  and  whose  properties  are  distinct  from  those  of  the  normal 
silver  ion  in  water.  So,  we  find  that  salts  of  this  ion  are  much  more 
soluble  than  those  of  the  normal  silver  ion,  particularly  in  the  case  of 
the  halides.  Similar  complexes  are  formed  in  the  case  of  many  other 
salts  dissolved  in  water  in  the  presence  of  ammonia,  as,  for  example, 
salts  of  copper,  zinc,  cobalt,  nickel,  etc.  The  distinctive  properties  of 
the  complex  affect  all  the  characteristic  properties  of  the  resulting  elec- 
trolytic solution.  So  the  addition  of  ammonia  to  a  solution  of  a  silver 
or  a  copper  salt  in  water  decreases  the  viscosity  of  the  solution,  until  all 


178        PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 


the  metal  has  been  transformed  to  the  complex.  This  behavior  is  due 
to  the  fact  that  the  solutions  of  this  complex  possess  a  negative  viscosity 
relative  to  that  of  pure  water,  while  solutions  of  the  original  salt  possess 
a  positive  viscosity  with  respect  to  pure  water. 

In  non-aqueous  solutions,  we  find  similar  relations;  that  is,  inter- 
action often  takes  place  between  the  second  solvent  component  and  the 
electrolyte.  Thus,  the  ionization  of  solutions  of  a  large  number  of  salts 
appears  to  be  greatly  affected  by  the  addition  of  a  small  amount  of  water. 
This  is  particularly  the  case  with  electrolytes  which  exhibit  a  marked 
tendency  to  form  complexes  with  water.  If  a  salt,  which  exhibits  a 
marked  tendency  to  form  hydrates,  is  dissolved  in  a  medium,  with 
which  this  salt  has  little  tendency  to  form  a  solvate  complex,  then 
the  salt  will  be  relatively  little  ionized  when  dissolved  in  this  solvent. 
On  addition  of  water  to  such  a  solution,  the  salt  apparently  forms  a 
complex  with  water,  whose  ionization  in  the  original  solvent  is  much 
greater  than  that  of  the  anhydrous  salt.  Solutions  of  potassium  chloride 
or  iodide,  for  example,  are  highly  ionized  in  acetone  and  their  ionization, 
and  consequently  their  conductance,  is  but  little  affected  by  the  addition 
of  water.  On  the  other  hand,  lithium  chloride,  which  shows  a  pronounced 
tendency  to  form  complexes  with  water,  is  ionized  to  only  a  relatively 
slight  degree  in  pure  acetone.  On  the  addition  of  water  to  a  solution 
of  a  lithium  salt  in  acetone,  the  conductance  is  greatly  increased.  Similar 
results  have  been  obtained  in  the  case  of  calcium  chloride. 

2.  Conductance  of  Salt  Solutions  on  the  Addition  of  Small  Amounts 
of  Water.  In  Table  LXIV  are  given  values  of  the  conductance  of  solu- 

TABLE   LXIV. 
CONDUCTANCE  OF  SALTS  IN  ANHYDROUS  PROPYL  ALCOHOL  AT  25 °.1 


Nal 


CX103 

0.0623 

0.1581 

0.3902 

0.6591 

1.498 

2.310 

5.890 

13.26 

27.77 

53.40 


Ca(N03)2  Anhydrous 
C  X  103  Amoi 


19.94 
19.36 
18.36 
17.72 
16.30 
15.40 
13.23 
11.28 
9.815 
8.400 


0.363 

0.792 

1.617 

3.326 

5.908 

7.247 

14.320 

24.930 

43.290 


5.140 
3.834 
2.894 
2.184 
1.798 
1.688 
1.258 
0.976 
0.772 


*Kraua  and  Bishop,  J.  Am.  Chem.  Soc.  43,  1568  (1921). 


ELECTROLYTES  IN  MIXED  SOLVENTS  179 

tions  of  calcium  nitrate  and  sodium  iodide  in  propyl  alcohol.  In  the 
case  of  calcium  nitrate  the  values  given  are  the  molecular  conductances 
whose  limit  at  low  concentration  should  be  approximately  twice  that  of 
the  equivalent  conductance.  It  will  be  observed  that  while  sodium  iodide 
is  highly  ionized,  calcium  nitrate  is  ionized  to  only  a  relatively  small 
extent. 

At  a  concentration  of  approximately  10~3  molal,  the  ionization  of  cal- 
cium nitrate  is  less  than  15  per  cent,  whereas  at  the  same  concentration 
sodium  iodide  is  very  largely  ionized.  If  the  equivalent  conductances  are 
plotted  against  the  concentrations,  the  curve  of  sodium  iodide  approaches 
a  limiting  form  asymptotically,  whereas  that  of  anhydrous  calcium  nitrate 
is  convex  toward  the  axis  of  concentrations,  the  increase  in  conductance 
being  the  greater  the  lower  the  concentration  of  the  electrolyte. 

The  addition  of  0.185  mols  of  water  per  liter  to  the  calcium  nitrate 
solution,  whose  concentration  was  0.045  N,  raised  the  conductance  from 
0.772  to  2.036,  and  an  additional  0.346  mols  raised  the  conductance  to 
2.991.  It  is  evident,  therefore,  that  the  addition  of  water  to  a  solution 
of  anhydrous  calcium  nitrate  in  propyl  alcohol  causes  a  large  increase 
in  the  ionization  of  the  salt.  This  follows,  since  the  viscosity  of  the 
solvent  is  not  materially  affected  by  the  addition  of  small  amounts  of 
water.  It  is  true  that,  if  a  complex  is  formed  on  the  addition  of  water 
to  a  solution  of  calcium  nitrate,  the  speed  of  the  ion  may  be  affected  by 
the  addition  of  water,  but  it  seems  likely  that,  if  anything,  the  speed  of 
the  complex  will  be  lower  than  that  of  the  original  ion.  However  this 
may  be,  it  is  very  unlikely  that  the  speed  of  the  complex  could  vary 
greatly  from  that  of  the  anhydrous  ion  and  the  resulting  change  in  the 
conductance  must  therefore  be  due  to  a  change  in  the  ionization  of  the 
electrolyte  as  a  result  of  the  formation  of  a  complex  with  water. 

TABLE    LXV. 

CONDUCTANCE  OF  Mg(N03)2.6H20  IN  ANHYDROUS  PROPYL  ALCOHOL  AND 
IN  PROPYL  ALCOHOL  CONTAINING  0.7  PER  CENT  WATER  AT  25°. 

Anhydrous  Solvent  Solvent  +  0.7%  Water 

CX103  Amoi.  CX103  A 

0.394  12.422  .298  17.774 

0.865  10.730  1.950  9.062 

1.942                 8.932  3.758  7.326 

3.483                  7.774  6.339  6.188 

6.406                 6.408  11.670  5.096 

9.804                  6.026  19.460  4.400 

19.89                   4.674  30.410  3.921 

36.12                   3.866  49.560  3.555 


180        PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

In  Table  LXV  are  given  values  for  the  conductance  of  magnesium 
nitrate  hexahydrate  in  anhydrous  propyl  alcohol  and  in  propyl  alcohol 
containing  0.7  per  cent  of  water. 

The  original  salt  having  been  hydrated,  it  is  probable  that  the  complex 
hydrate  was  to  some  extent  present  in  the  solution.  Nevertheless,  the 
value  of  the  molecular  conductance  is  of  the  same  order  of  magnitude 
as  that  of  anhydrous  calcium  nitrate  in  propyl  alcohol  and  the  conduct- 
ance curve  is  of  the  same  general  form.  On  the  addition  of  water,  the 
conductance  of  the  magnesium  nitrate  is  markedly  increased,  particularly 
in  the  more  dilute  solutions.  The  curve  for  the  conductance  in  the 
presence  of  water  twice  intersects  the  curve  for  the  conductance  in  the 
anhydrous  solvent.  This  effect  may  in  part  be  due  to  a  change  in  the 
speed  of  the  ions,  owing  to  the  presence  of  water,  and  in  part  to  a  more 
or  less  complex  equilibrium  which  must  exist  between  the  dissolved 
electrolyte  and  the  water. 

Those  salts  which  have  only  a  slight  tendency  to  form  stable  com- 
plexes with  water  are,  as  a  rule,  ionized  more  highly  in  such  solvents  as 
acetone  and  the  alcohols  than  are  salts  which  exhibit  a  pronounced  ten- 
dency to  form  stable  complexes  with  water.  Correspondingly,  the  addi- 
tion of  water  to  a  solution  of  a  salt,  which  has  little  tendency  to  form 
complexes  with  water,  has  very  little  influence  upon  its  ionization.  The 
effect  is  scarcely  observable  in  solutions  of  such  salts  as  potassium  and 
sodium  iodides.  In  the  case  of  lithium  chloride  dissolved  in  ethyl  alcohol 
there  is  a  slight  increase  in  the  ionization  upon  the  addition  of  water. 
In  Table  LXVI  are  given  values  for  the  conductance  of  solutions  of 
lithium  chloride  in  ethyl  alcohol  in  the  presence  of  water.2  It  is  evident 
from  an  inspection  of  this  table  that  the  conductance  of  lithium  chloride 
in  ethyl  alcohol  is  increased  slightly  upon  the  addition  of  water.  The 
effect  is  somewhat  more  marked  at  higher  concentration. 

TABLE    LXVI. 

CONDUCTANCE  OF  LiCl  IN  C2H5OH  IN  THE  PRESENCE  OF  WATER  AT  25°. 


0 

A  517'7 

A J31.8 

«  Goldschmidt,  Ztschr.  /.  phya.  Chem.  89,  138   (1914). 


Dilution 

of 

pjMols  per  Liter 
.2w 

Electrolyte 

1                 2 

10 

V 

18.8            19.7 

24.2 

20 

32.2            32.8 

33.1 

640 

ELECTROLYTES  IN  MIXED  SOLVENTS  181 

3.  The  Conductance  of  the  Acids  in  Mixtures  of  the  Alcohols  and 
Water.  In  aqueous  solutions,  the  acids  and  bases  occupy  a  unique  posi- 
tion in  that  their  solutions  possess  properties  which,  as  a  rule,  differen- 
tiate them  sharply  from  solutions  of  typical  salts.  The  acids  and  bases 
in  water  are  the  only  electrolytes  which  apparently  conform  to  the  mass- 
action  law  in  this  solvent.  Furthermore,  the  ionization  of  different  acids 
and  bases  differs  greatly,  while  that  of  salts  of  the  same  type  is  prac- 
tically the  same  at  all  concentrations.  So,  also,  the  speed  of  the  hydrogen 
and  hydroxyl  ions  is  much  greater  than  that  of  the  ordinary  ions  at  ordi- 
nary temperatures.  In  the  case  of  acids,  at  any  rate,  many  facts  indicate 
an  interaction  between  acid  and  water  whereby  a  complex  positive  ion 
is  formed. 

In  Table  LXVII  are  given  conductance  values  for  solutions  of  hydro- 
chloric acid  in  methyl  alcohol  in  the  presence  of  varying  amounts  of 
water.8 

TABLE   LXVII. 

CONDUCTANCE  OF  HYDROCHLORIC  ACID  IN  METHYL  ALCOHOL  IN  THE 
PRESENCE  OF  VARYING  AMOUNTS  OF  WATER  AT  25°. 


A., 


The  effect  of  adding  water  to  a  solution  of  hydrochloric  acid  in 
methyl  alcohol  is  to  greatly  decrease  the  conductance  of  the  solution  and 
this  effect  is  relatively  independent  of  the  concentration  of  the  solute. 
It  appears,  therefore,  that  the  ionization  of  hydrochloric  acid  is  not 
materially  affected  by  the  addition  of  water,  but  that  the  speed  of  the 
hydrogen  ion  is  greatly  reduced.  It  is  true  that  on  the  addition  of  water 
to  methyl  alcohol  the  viscosity  is  increased,  but  the  viscosity  change  due 
to  the  small  amounts  of  water  added  in  the  case  of  these  solutions  is 
inconsiderable  and  cannot  account  for  the  large  decrease  in  the  conduct- 
ance of  these  solutions.  Apparently,  therefore,  the  change  in  conduct- 
ance is  due  to  a  slowing  up  of  the  hydrogen  ion,  since  it  is  known  that 
the  chloride  ion  is  normal  in  its  behavior  in  mixtures  of  alcohol  and 
water.  The  values  given  for  the  limiting  value  of  the  equivalent  con- 
ductance are  approximate,  since  the  extrapolation  function  employed  in 
determining  these  values  is  uncertain. 

»  Goldschmidt  and  Thuesen,  Ztschr.  f.  phya.  Chem.  81,  32  (1913). 


Mols 

of  H20  per  Liter 

Cone,  of 

0 

0.1 

0.2 

0.5 

1.0 

2.0 

Electrolyte 

J  115.4 

99.6 

91.3 

81.6 

78.1 

67.1 

0.10 

(171.9 

141.7 

129.3 

120.8 

116.7 

97.8 

0.0015625 

192. 

157. 

143. 

135. 

130. 

107. 

0.00 

182        PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

Apparently,  when  water  is  added  to  a  solution  of  hydrochloric  acid 
in  methyl  alcohol,  a  complex  is  formed  with  water  which  moves  with  a 
much  lower  speed  than  does  the  normal  hydrogen  ion  in  pure  methyl 
alcohol.  It  will  be  noted  that  the  speed  of  the  normal  hydrogen  ion  in 
methyl  alcohol  is  exceptionally  high.  The  A0  values  for  typical  salts 
in  this  solvent  lie  in  the  neighborhood  of  100.  The  hydrogen  ion  must 
therefore  move  with  a  speed  roughly  three  times  that  of  the  chloride  or 
potassium  ion. 

Solutions  of  hydrochloric  acid  in  ethyl  alcohol  exhibit  a  similar 
behavior  on  the  addition  of  water.4  Values  of  the  equivalent  conduct- 
ance of  hydrochloric  acid  in  ethyl  alcohol  in  the  presence  of  varying 
amounts  of  water  are  given  in  Table  LXVIII. 

TABLE  LXVIII. 

CONDUCTANCE  OF  SOLUTIONS  OF  HYDROCHLORIC  ACID  IN  ETHYL  ALCOHOL 
IN  THE  PRESENCE  OF  WATER  AT  25°. 

Mols  of  H20  per  Liter 
0    0.028    0.05     0.1     0.2      0.5       1.0      2.0      3.0    Dilution 


74.2    63.2    58.5    52.6    47.4    42.8    41.8    42.4    44.4        1280 
35.0    32.0    30.4    27.5    24.2    21.3    21.4    23.3    26.1         10 
89.4    75.1     69.3     62.0    56.0    50.5    48.5    48.2    49.5         oo 


The  conductance  curve  passes  through  a  minimum  for  a  solution  contain- 
ing approximately  two  mols  of  water  per  liter.  This  minimum  is  slightly 
affected  by  the  concentration  of  the  acid.  At  lower  concentrations  the 
minimum  occurs  at  a  slightly  higher  concentration  of  water.  The  shift 
in  the  minimum  point,  following  a  change  in  the  concentration  of  the 
acid,  may  in  part  be  due  to  a  change  in  the  viscosity  of  the  solution  due 
to  the  addition  of  acid.  On  the  other  hand,  it  is  possible  that  the  ioniza- 
tion  of  the  salt  is  materially  affected  by  the  presence  of  water,  particu- 
larly at  the  higher  concentrations.  It  may  be  assumed,  however,  that 
at  very  low  concentrations  of  acid,  the  ionization  is  not  materially 
changed  due  to  the  addition  of  water.  If  this  is  true,  and  the  acid  is 
highly  ionized,  the  A0  values  should  follow  a  curve  corresponding  approxi- 
mately to  that  of  the  most  dilute  solution.  In  other  words,  the  A0  values 
should  pass  through  a  minimum  somewhere  between  1  and  2  normal 
with  respect  to  water,  which  has  been  found  to  be  the  case.  This  indi- 
cates that  the  addition  of  water  results  in  an  initial  decrease  in  the 
speed  of  the  ions  up  to  a  concentration  of  about  2  normal,  and  there- 
after in  an  increase  on  further  addition  of  water. 

« Goldschmidt,  Ztschr.  f.  phya.  Chem.  89,  132   (1914). 


ELECTROLYTES  IN  MIXED  SOLVENTS  183 

This  is  further  indicated  by  results  at  higher  concentrations  of  water. 
In  the  following  table  are  given  values  for  the  conductance  of  hydro- 
chloric acid  in  mixtures  of  water  and  ethyl  alcohol  at  25°  for  larger 
amounts  of  water.5 

TABLE   LXIX. 

CONDUCTANCE  OP  SOLUTIONS  OF  HYDROCHLORIC  ACID  IN  ALCOHOL  IN  THE 
PRESENCE  OF  WATER  AT  25°. 

Equivalent  Conductances  at  Dilutions 
CH20  F  =  12  F  =  48  F=oo 

0.0                        34.3  43.6                      67. 

6.83                      37.2  43.0                      51. 

13.85                      60.3  65.8                      75.5 

27.68  115.  121.  130. 

41.57  207.  218.  230.5 

The  values  for  the  pure  solvent  do  not  agree  with  those  given  in  Table 
LXVIII.  It  is  possible  that  the  values  in  this  case  are  low  owing  to 
the  presence  of  traces  of  water.6  However,  it  is  evident  that,  in  the 
presence  of  water  at  higher  concentrations,  the  conductance  increases  with 
addition  of  water.  This  may  be  due,  in  part,  to  an  increased  ionization, 
but  it  appears  probable  that  it  is  also  in  part  due  to  an  increase  in  the 
speed  of  the  hydrogen  ion.  That  a  complex  between  water  and  the 
hydrogen  ions  is  initially  formed  is  likewise  indicated  by  other  prop- 
erties of  these  solutions  such  as  the  catalytic  effects  due  to  the  hydro- 
gen ion.7 

In  the  case  of  the  weaker  acids,  on  addition  of  water,  the  conductance 
curve  is  modified  the  more  the  weaker  the  acid.  In  Table  LXX  are  given 
values  for  the  conductance  of  sulphosalicylic  acid  in  ethyl  alcohol.8  In 
solutions  of  sulphosalicylic  acid,  there  is  a  marked  decrease  in  the  con- 
ductance on  addition  of  small  quantities  of  water  up  to  normal  concen- 
tration, but  the  effect  is  not  as  great  as  it  is  in  solutions  of  hydrochloric 
acid. 

TABLE    LXX. 

CONDUCTANCE  OF  SULPHOSALICYLIC  ACID  IN  C2H5OH  AT  25°  IN  THE 
PRESENCE  OF  WATER.    V  =  160. 

CHQ  ....       0  .003        .019          .1  .2  .5  1.0 


49.0        49.0        45.4        37.0        32.8        29.9        29.5 


"Kailan,  Ztsclw.  /.  phys.  Cliem.  89,  678  (1914). 
•  Kailan,  loc.  cit. 

7  Goldschmidt  and  Thuesen,  loc.  cit.f  p.  62. 

8  Goldschmidt,  Ztschr.  f.  phys.  Chem.  89,  139   (1914). 


184        PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

In  the  following  table  are  given  values  for  the  conductance  of  picric 
acid  in  methyl  alcohol  in  the  presence  of  water.9 

TABLE    LXXI. 

CONDUCTANCE  OF  PICRIC  ACID  IN  CH3OH  AT  25°  IN  THE 
PRESENCE  OF  WATER. 

Concentration  of  Water  Cone. 

0  .5  1.  2.  of  Acid 

9.32          12.7          16.3          23.4          0.1 
56.73          63.7          70.2          75.7          0.0015625 

In  this  case,  the  conductance  effect  due  to  addition  of  water  is  the  reverse 
of  that  in  solutions  of  stronger  acids.  The  conductance  increases 
throughout  as  the  concentration  of  water  increases.  It  is  evident  that 
the  ionization  of  picric  acid  is  much  smaller  than  that  of  the  stronger 
acids.  The  increase  in  the  conductance  at  the  higher  concentration  is 
much  more  marked  than  it  is  at  the  lower  concentration,  indicating  that 
at  higher  concentration,  at  least,  an  increase  in  the  ionization  due  to  the 
addition  of  water  is  a  primary  factor  in  causing  an  increase  in  the  con- 
ductance of  the  solution.  It  may  be  presumed  that  the  speed  of  the 
hydrogen  ion  is  independent  of  the  nature  of  the  acid,  and  that  conse- 
quently the  A0  values  for  picric  acid  decrease  with  increasing  amounts 
of  water,  until  fairly  high  concentrations  are  reached.  In  the  following 
table  are  given  approximate  values  of  A0  for  picric  acid  dissolved  in 
methyl  alcohol  in  the  presence  of  water.10 

TABLE   LXXII. 

CHANGE  OF  A0  FOR  PICRIC  ACID  IN  METHYL  ALCOHOL  WITH  VARYING 
AMOUNTS  OF  WATER. 

CH20  0  .5  1.  2. 

A  182  108  98  90 

These  values  of  A0,  while  only  approximate,  nevertheless  cannot  differ 
greatly  from  the  true  values  and  clearly  indicate  that  the  increase  in 
the  conductance  of  picric  acid  is  due  to  an  increased  ionization  of  the 
acid  as  a  result  of  the  presence  of  water. 

In  solutions  of  weaker  acids,  the  effect  of  water  on  the  ionization  of 
the  acid  is  even  more  pronounced.  In  the  following  table  are  given 
values  for  trichlorobutyric  acid:  11 

•  Goldschmidt  and  Thuesen,  loc.  cit.f  p.  35 
10  Ibid.,  loc.  tit. 
n/6id.,  loc.  cit.f  p.  37. 


ELECTROLYTES  IN  MIXED  SOLVENTS  185 

TABLE  LXXIII. 

CONDUCTANCE  OF  0.2  N  TRICHLOROBUTYRIC  ACID  IN  CH3OH  IN  THE 
PRESENCE  OF  WATER. 

0  10  2.0 

A  0.446  0.825  1.283 

In  a  0.2  normal  solution  of  this  acid  the  conductance  is  increased  100 
per  cent  on  the  addition  of  one  mol  of  water.  In  other  words,  the  ioniza- 
tion  is  increased  somewhat  over  100  per  cent  by  this  addition  of  water. 
In  this  respect  the  acids  behave  in  a  manner  similar  to  that  of  typical 
salts  which  have  a  great  tendency  to  form  hydrates. 

The  effect  of  water  on  the  ionization  of  the  weaker  acids  is  clearly 
shown  in  the  increased  value  of  the  ionization  constants  of  these  acids 
on  addition  of  water.  In  Table  LXXIV  are  given  values  of  the  ioniza- 
tion constant 12  for  trichloroacetic  acid  in  absolute  alcohol  and  in  alcohol 
containing  0.622  mols  of  water  at  different  dilutions.  Excepting  at  the 
highest  concentrations,  the  constant  varies  but  little  with  the  concentra- 
tion of  the  acid. 

TABLE  LXXIV. 

IONIZATION  CONSTANT  OF  TRICHLOROACETIC  ACID  IN  ALCOHOL  IN  THE 
ABSENCE  AND  IN  THE  PRESENCE  OF  WATER. 

K  X  10-6 
V  Pure  Alcohol    CR  Q  =  0.622  N 

5.5  5.03  31.1 

11.  4.74  29.3 

22.  4.45  28.6 

44.  4.45  27.6 

88.  4.50  27.6 

176.  —  28.4 

It  is  evident  that,  due  to  the  addition  of  0.622  mols  of  water,  the 
ionization  constant  of  trichloroacetic  acid  is  increased  approximately  six 
times.  Corresponding  to  this  increase  in  the  value  of  the  ionization  con- 
stant of  the  acid,  the  conductance  of  the  acid  is  obviously  greatly 
increased.  The  effect  of  water  on  the  conductance  of  different  electro- 
lytes is  shown  in  Figure  41.  The  great  percentage  increase  in  the  con- 
ductance of  trichloroacetic  acid  will  be  noted  in  contrast  to  a  smaller 
increase  in  the  case  of  picric  acid  and  lithium  chloride  and  a  large  decrease 
in  that  of  hydrochloric  acid. 

"Braune,  Ztschr.  f.  phys.  Chem.  85,  170  (1913). 


186        PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

It  seems  fairly  clear  that,  on  the  addition  of  water  to  a  solution  of 
an  acid  in  alcohol,  a  complex  is  formed  between  the  acid  and  the  added 
water.  The  hydrogen  ion  of  this  complex  moves  with  a  speed  much 
lower  than  that  of  the  normal  hydrogen  ion  in  alcohol  or  in  pure  water. 
In  the  case  of  the  weaker  acids,  the  ionization  of  the  hydrated  acid  is 


i.o 

Mols  of  Water. 


3.0 


FIG.  41.    Illustrating  the  Influence  of  Water  on  the  Conductance  of  Different 
Electrolytes  in  Ethyl  Alcohol. 

much  greater  than  that  of  the  unhydrated  acid.  In  solutions  of  salts  in 
non-aqueous  solvents,  there  is,  as  we  have  seen,  a  similar  increase  in 
ionization  on  the  addition  of  water  in  the  case  of  those  salts  which  exhibit 
a  pronounced  tendency  to  form  complexes  with  water.  In  these  cases, 
therefore,  the  process  of  ionization  is  intimately  connected  with  the 
formation  of  a  more  or  less  definite  complex,  and  since  these  complexes 
are  formed  on  the  addition  of  a  small  amount  of  water  to  solutions  in 


ELECTROLYTES  IN  MIXED  SOLVENTS  187 

anhydrous  solvents,  there  is  all  the  more  reason  for  believing  that  these 
complexes  exist  when  the  salts  are  dissolved  in  pure  water. 

4.  Conductance  in  Mixed  Solvents  over  Large  Concentration  Ranges. 
A  considerable  number  of  systems  have  been  studied  in  which  salts 
have  been  dissolved  in  mixtures  of  two  solvents  miscible  in  all  propor- 
tions. In  these  solutions  the  conductance  has  not  been  studied  for  small 
additions  of  either  component.  As  a  rule,  the  concentration  was  varied 
by  intervals  of  25  per  cent.  In  such  cases,  the  change  in  the  viscosity  of 
the  medium,  as  well  as  that  in  the  ionization  of  the  electrolyte,  makes 
itself  felt. 

When  the  two  solvents  have  approximately  the  same  dielectric  con- 
stant and  the  dissolved  salts  are  ionized  to  practically  the  same  extent 
in  the  two  solvents,  then  the  conductance  of  solutions  in  mixtures  of  these 
solvents  is  determined  primarily  by  the  viscosity  of  the  mixtures.  In 
other  cases,  where  the  viscosity  change  is  small  and  the  ionization  of  the 
salt  in  the  two  solvents  differs  greatly,  the  form  of  the  curve  is  largely 
dependent  upon  the  ionization  change  brought  about  by  the  change  in 
the  composition  of  the  mixture. 

In  Figure  42  are  shown  values  of  the  fluidity  of  mixtures  of  acetone 
with  water,  methyl  and  ethyl  alcohol  at  0°.1S  In  Figure  43  are  shown 
fluidity  curves  for  mixtures  of  methyl  alcohol  with  water  and  ethyl 
alcohol/4  and  nitrobenzol  with  methyl  and  ethyl  alcohols,15  at  25°.  The 
values  are  given  in  Table  LXXV.  In  the  case  of  these  curves  the  precise 

TABLE   LXXV. 

THE  FLUIDITY  OF  MIXTURES  AS  A  FUNCTION  OF  THEIR  COMPOSITION. 
Solvent  Per  Cent  B 


=  0 


A 

B 

0 

25 

50 

75 

100 

H2O 

Acetone  .  .  . 

56.24 

34.12 

33.03 

58.80 

244.1' 

CH3OH 
C2H5OH 

Acetone  .  .  . 
Acetone  .  .  . 

122.2 
53.88 

153.9 
96.08 

187.4 
147.0 

222.2 
200.4 

244.1  [ 
244.1J 

H20 

CH3OH 

112.3 

76.18 

67.72 

83.6 

144.4 

H20 

C2H5OH  .. 

112.3 

55.22 

41.56 

47.21 

87.4 

C6H5N02 

CH3OH   ... 

54.29 

84.4 

110.9 

142.3 

166.4 

C6KLN02 

C2H5OH  .. 

54.3 

73.3 

82.7 

88.2 

87.4 

C2H5OH 

CH3OH   ... 

87.36 

105.5 

124.9 

147.3 

164.4 

values  are  represented  only  for  the  pure  solvents  and  the  mixtures  hav- 
ing compositions  of  25,  50  and  75  per  cent,  smooth  curves  having  been 

"Jones,  Bingham  and  McMaster,  ZtscJir.  f.  phys.  CJiem.  57,  193   (1906). 
"Jones  and  Veazey,  Conductivity  and  Viscosity  in  Mixed  Solvents,  Carnegie  Reports, 
p.  190   (1907). 

"Jones  and  Veazey,  Ztsctir.  f.  phys.  Chem.  62,  49  (1908). 


188        PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 


drawn  through  these  points.  At  intermediate  concentrations  the  true 
curves  may  vary  considerably  from  the  curves  as  drawn,  particularly  at 
concentrations  in  the  neighborhood  of  the  axes.  Nevertheless,  the  curves 
show  in  a  general  way  the  relation  between  the  fluidity  and  the  com- 
position of  these  mixtures.  The  fluidity  curves  of  all  mixtures  in  which 


25 


50 


IS 


too 


Per? 


FIG.  42. 


Representing  the  Fluidity  of  Mixtures  of  Acetone  with  Various  Solvents  at 
0°  as  a  Function  of  Composition. 


water  is  one  component  are  characterized  by  a  pronounced  minimum, 
which  lies  roughly  at  a  composition  of  50  per  cent.  When  the  fluidity 
of  the  second  solvent  differs  greatly  from  that  of  water,  the  minimum 
is  displaced  in  the  direction  of  the  solvent  having  the  lower  fluidity.  In 
mixtures  of  solvents  of  the  same  type,  such  as  methyl  and  ethyl  alcohols, 
as  well  as  in  mixtures  of  the  alcohols  and  nitrobenzol,  or  the  alcohols  and 
acetone,  the  curves  approach  more  -or  less  closely  to  straight  lines,  the 
viscosity  of  the  mixture  being  throughout  intermediate  between  that  of 


ELECTROLYTES  IN  MIXED  SOLVENTS 


189 


the  two  components.    When  the  two  components  have  nearly  the  same 
fluidity,  the  fluidity  curve  exhibits  a  slight  minimum. 

It  is  apparent  that  the  fluidities  of  mixtures  in  general  differ  con- 
siderably from  those  of  the  pure  components  and  it  is  to  be  expected  that 
the  conductance  of  solutions  in  such  mixtures  will  be  materially  affected 
by  the  viscosity  change  of  the  solvent.  In  those  cases  in  which  the  elec- 


SO 


7S 


/CO 

B 


FIG.  43.    Fluidity  of  Various  Mixtures  at  25°. 

trolyte  is  largely  ionized,  it  is  to  be  expected  that  the  conductance  of  a 
solution  in  a  mixture  of  two  solvents  will  vary  approximately  in  accord- 
ance with  the  fluidity  of  the  mixture.  At  higher  concentrations  a  similar 
correspondence  between  the  conductance  and  the  fluidity  is  to  be  expected 
when  the  ionization  of  the  electrolyte  is  the  same  in  the  two  solvents.  In 
general,  this  will  be  the  case  when  we  have  solvents  which  have  the  same 
dielectric  constant,  and  an  electrolyte  which  does  not  exhibit  a  marked 
tendency  to  form  solvates.  In  other  cases,  when  the  ionization  is 


190        PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 


largely  dependent  upon  the  formation  of  solvates  between  the  electrolyte 
and  one  or  the  other  of  the  solvent  components,  the  ionization  of  the 
salt  in  the  mixture,  rather  than  the  fluidity  of  the  mixture,  will  determine 
the  form  of  the  conductance  curve  and  this  will  be  the  more  true,  the 
more  nearly  the  fluidity  curves  are  linear  functions  of  the  composition. 

In  Figure  44  are  shown  conductance  curves  for  solutions  of  tetra- 
ethylammonium  iodide  in  mixtures  of  water 16  with  methyl  and  with 


100 


50 


o 
A. 


Per  Cent  of  Component  B. 


FIG.  44.     Conductance  of  Tetraethylammonium  Iodide  in  Solvent  Mixtures  at  25° 

at  7  =  800. 

ethyl  alcohol,  nitrobenzol 17  with  methyl  and  with  ethyl  alcohol,  and 
methyl  with  ethyl  alcohol.16  The  data  from  which  the  curves  are  drawn 
are  given  in  Table  LXXVI. 

Comparing  the  conductance  curves  with  the  fluidity  curves,  it  is  clear 
that  in  these  solutions  of  tetraethylammonium  iodide  there  is  a  close 
correspondence  between  the  two.  The  conductance  curves  for  mixtures 
of  methyl  alcohol,  ethyl  alcohol  and  nitrobenzol  correspond  very  closely 
with  the  fluidity  curves.  So,  also,  in  mixtures  of  water  with  ethyl  and 

18  Jones,  Bingham  and  McMaster,  loc.  cit.f  p.  257. 
"  Jones  and  Veazey,  loc.  cit.,  p.  44. 


ELECTROLYTES  IN  MIXED  SOLVENTS  191 

TABLE  LXXVI. 

CONDUCTANCE  OF  TETRAETHYLAMMONIUM  IODIDE  IN  MIXED  SOLVENTS 
AT  25°  AT  A  DILUTION  OF  800  LITERS. 

Solvent  Per  Cent  B 


A 

B 

0 

25 

50 

75 

100 

H20 

CH3OH    . 

..  100.6 

67.03 

55.17 

62.50 

105.3 

H2O 

C2H5OH 

...  100.6 

54.53 

38.68 

35.51 

41.46 

C6H5N02 

CH3OH   . 

.  .     31.44 

47.91 

63.54 

80.53 

105.3 

C6H5N02 

C2H5OH 

...    31.34 

37.88 

41.87 

43.51 

41.46 

C2H5OH 

CH3OH    . 

.  .     41.46 

55.20 

69.44 

84.22 

105.3 

methyl  alcohols,  a  pronounced  minimum  is  found  in  both  conductance 
curves.  Finally,  in  mixtures  of  nitrobenzol  and  ethyl  alcohol,  the  con- 
ductance curve  exhibits  a  slight  maximum  corresponding  with  the  maxi- 
mum in  the  fluidity  curve.  In  general,  salts  which  show  little  tendency 
to  form  stable  complexes  with  water,  in  other  words,  those  salts  which 
exhibit  a  negative  viscosity  in  aqueous  solutions,  yield  conductance 
curves  closely  resembling  those  for  tetraethylammonium  iodide.  It  may 
be  noted,  however,  that  the  conductance  for  tetraethylammonium  iodide 
in  methyl  alcohol  is  abnormally  high,  being  in  fact  somewhat  greater 
than  that  of  the  same  salt  in  water.  In  general,  the  conductance  of  salts 
in  methyl  alcohol  is  somewhat  lower  than  that  of  salts  in  water,  even 
though  the  viscosity  of  water  is  greater  than  that  of  methyl  alcohol.  The 
curves  for  solutions  of  other  binary  salts  do  not  differ  materially  from 
those  of  tetraethylammonium  iodide.  In  the  case  of  electrolytes  of  this 
type,  the  ionization  in  a  given  solvent  is  near  the  maximum  and  is  not 
appreciably  affected  by  the  addition  of  a  small  amount  of  another  solvent. 
Moreover,  the  ionization  of  typical  salts  in  these  solvents  does  not  differ 
greatly  at  concentrations  approaching  10~3  normal.  The  form  of  the 
conductance  curves,  therefore,  is  determined  primarily  by  the  fluidity 
of  the  solvent  mixtures. 

TABLE  LXXVII. 

CONDUCTANCE  OF  SOLUTIONS  OF  POTASSIUM   IODIDE  IN  MIXTURES  OF 
ACETONE  WITH  METHYL  AND  ETHYL  ALCOHOLS  AND  WATER  AT  0°. 

Per  Cent  Acetone  0  25  50  75            100 

H20   78.0  47.8  37.5  44.1  120.01 

CH3OH   71.7  83.9  94.1  106.5  120.0^7  =  1600 

C2H5OH    28.6  40.1  61.3  84.8  120.0J 

H20   76.7        44.6        36.3          41.6        100.41 

CH3OH  65.7        74.1        82.7          93.1        100.417  = 

C2H5OH    22.0        35.5        52.2          72.0        100.4J 


192     PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 


In  Table  LXXVII  are  given  values  for  the  conductance  of  potassium 
iodide  at  0°  in  mixtures  of  acetone  with  methyl  and  ethyl  alcohols  and 
water 18  at  the  concentrations  V  =  1600  and  V  =  200.  The  results  are 
shown  graphically  in  Figure  45.  It  is  apparent  that  in  solutions  of  potas- 
sium iodide  in  mixtures  containing  acetone,  the  general  form  of  the  con- 
ductance curves  corresponds  with  that  of  the  fluidity  curves.  However, 
the  deviations  from  the  fluidity  curves  in  these  solutions  are  considerably 


V--ZQO 


as  so 

Per  Cent  Acetone. 


too 


FIG.  45. 


Conductance  of  Potassium  Iodide  in  Acetone  Mixtures  at  Oc 
V  =  200  and  V  =  1600. 


at  Dilutions 


greater  than  in  solutions  of  tetraethylammonium  iodide  in  mixtures  of 
the  alcohols  and  water.  This  is  doubtless  due  to  the  relatively  low 
ionizing  power  of  acetone  and  its  selective  action  upon  different  electro- 
lytes, as  well  as  upon  the  exceptionally  high  value  of  the  fluidity  of  pure 
acetone  with  respect  to  that  of  the  other  solvents.  The  concentration 
change  from  a  dilution  of  1600  to  200  has  only  an  immaterial  influence 
upon  the  form  of  the  curves. 

The  ionization  of  acetone  solutions  of  salts  which  exhibit  a  marked 
tendency  to  form  complexes  with  water,  or  other  solvents,  is  very  low. 
Under  these  conditions,  the  change  in  the  ionization  of  the  electrolyte  due 

"  Jones,  Bingham  and  McMaster,  loo.  cit.,  p.  193. 


ELECTROLYTES  IN  MIXED  SOLVENTS 


193 


to  the  addition  of  a  second  solvent  becomes  apparent.  In  Table 
LXXVIII  are  given  values  for  the  conductance  of  lithium  bromide  in 
mixtures  of  acetone  with  methyl  and  ethyl  alcohols  and  water.19 

TABLE  LXXVIII. 

THE  CONDUCTANCE  OF  LITHIUM  BROMIDE  IN  MIXTURES  OF  ACETONE 
WITH  METHYL  AND  ETHYL  ALCOHOLS  AND  WATER  AT  0°. 

Per  Cent  Acetone  0 

H20   56.12 

CH3OH  57.63 

C2H5OH    20.79 

H2O   47.25 

CH3OH  35.92 

C2H5OH    10.55 

The  results  are  shown  graphically  in  Figure  46.  An  examination  of 
the  curves  shows  a  very  complex  behavior  on  the  part  of  these  solutions 
compared  with  that  of  solutions  of  potassium  iodide  in  the  same  solvents. 
In  mixtures  of  acetone  and  methyl  alcohol,  at  the  lower  concentration, 


25 

50 

75 

100 

35.71 

28.34 

31.65 

70.891 

60.38 

67.02 

84.15 

70.89  U 

r=1600 

29.21 

50.98 

66.28 

70.89J 

28.82 

21.70 

24.00 

11.911 

35.03 

34.27 

29.77 

11.9UT* 

r  =  10 

14.72 

19.23 

19.16 

11.91 

CH50H 


CHjOH 


too 


V*  JO 


O  2ST  SO  75  100 

Per  Cent  Acetone. 

FIG.  46.    Conductance  of  Lithium  Bromide  in  Acetone  Mixtures  at  0°  at 

V  =  10  and  V  =  1600. 
»  Jones,  Bingham  and  McMaster,  loc.  cit.,  p.  257. 


194        PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

the  conductance  curve  exhibits  a  pronounced  maximum.  The  curve  for 
ethyl  alcohol  mixtures  exhibits  a  pronounced  inflection  point,  while  that 
for  water  merely  exhibits  a  minimum  corresponding  to  the  minimum  in 
the  fluidity  curve  of  the  mixtures  of  acetone  and  water.  At  the  higher 
concentration,  the  curve  for  water  initially  rises  steeply  to  a  very  flat 
maximum  and  minimum,  after  which  it  rises  with  increasing  concentra- 
tion of  water,  the  curve  corresponding  roughly  to  the  fluidity  curve  of  the 
mixtures  within  the  region  of  these  compositions.  The  conductance  of 
solutions  in  mixtures  of  acetone  and  methyl  alcohol  rises  sharply  for 
initial  additions  of  methyl  alcohol,  after  which  it  remains  practically 
constant  until  the  axis  of  the  pure  methyl  alcohol  is  reached.  With  ethyl 
alcohol  the  conductance  likewise  increases  markedly  for  the  initial  addi- 
tions. Thereafter,  the  curve  passes  through  a  maximum,  after  which  it 
gradually  diminishes  to  the  final  value  of  the  conductance  in  pure  ethyl 
alcohol.  It  is  only  in  solutions  in  which  the  percentage  of  ethyl  alcohol 
has  fallen  as  low  as  25  per  cent  that  the  curves  begin  to  approach  in  form 
the  fluidity  curves  of  the  mixtures.  For  mixtures  containing  larger 
amounts  of  acetone  the  form  of  the  curve  is  due  largely  to  the  change  in 
the  ionization  of  the  electrolyte.  On  the  addition  of  a  second  solvent  to 
acetone,  the  ionization  of  lithium  bromide  is  greatly  increased.  In  the 
water  mixtures,  the  viscosity  is  increased  so  greatly  for  small  additions 
of  this  solvent  that  the  conductance  diminishes.  In  the  case  of  methyl 
alcohol,  however,  the  fluidity  is  only  slightly  reduced  by  the  addition  of 
alcohol  and  consequently  the  conductance  curve  rises  initially  due  to  the 
increased  ionization  of  the  salt.  At  higher  concentrations  of  alcohol, 
however,  the  increasing  viscosity  of  the  solvent  finally  makes  itself  felt 
and  the  conductance  again  falls.  At  the  higher  concentration  of  the  salt, 
the  addition  of  water  causes  a  sufficient  increase  in  the  ionization  of  the 
electrolyte  to  overbalance  the  decrease  due  to  the  decreasing  fluidity  of 
the  mixture.  Initially,  therefore,  the  conductance  curve  for  lithium 
bromide  in  the  mixture  increases  with  the  addition  of  water,  passing 
through  a  slight  maximum,  after  which  the  curve  approximates  the 
fluidity  curve  of  the  solvent. 

As  a  rule,  higher  types  of  salts  are  ionized  to  a  much  smaller  extent 
than  are  binary  electrolytes,  particularly  the  salts  of  metals  which  exhibit 
a  pronounced  tendency  to  form  solvates  with  water.  In  Table  LXXIX 
are  given  values  for  the  conductance  of  calcium  nitrate  in  mixtures  of 
acetone  with  methyl  and  ethyl  alcohols  and  water.20 

The  relation  between  the  conductance  and  the  composition  of  these 
mixtures  is  shown  graphically  in  Figure  47.  It  is  evident  that  solutions 
of  calcium  nitrate  in  mixtures  containing  acetone  present  a  very  complex 

*>  Jones,  Bingham  and  McMaster,  loc.  tit.,  p.  193. 


ELECTROLYTES  IN  MIXED  SOLVENTS 


195 


25 

50 

75 

100 

80.0 

66.2 

76.7 

10.361 

82.6 

79.2 

64.2 

10.36  \V  = 

1600 

31.6 

38.0 

36.2 

10.36J 

55.0 

42.2 

31.3 

4.44] 

17.76 

13.82 

8.10 

4.44  \V  = 

10 

6.01 

6.00 

4.80 

4.44J 

TABLE  LXXIX. 

CONDUCTANCE  OF  SOLUTIONS  OF  CALCIUM  NITRATE  IN  MIXTURES  OP 
ACETONE  WITH  METHYL  AND  ETHYL  ALCOHOLS  AND  WATER  AT  0°. 

Per  Cent  Acetone      0 

H20   128.3 

CH3OH   77.2 

C2H5OH    18.81 

H90   89.8 

CH3OH  18.98 

C2H5OH    5.13 

relation  between  conductance  and  composition.  This  is  particularly  true 
of  the  acetone-water  mixtures.  Solutions  of  calcium  nitrate  in  acetone 
are  ionized  to  a  very  slight  extent,  even  at  high  dilutions.  The  limiting 
equivalent  conductance  of  binary  electrolytes  in  acetone  has  a  value  of 
approximately  170.  The  limiting  value  of  the  equivalent  conductance  of 


tsro 


HtO 


V=  1600 


50  7S 

Per  Cent  Acetone. 


100 


FIG.  47.    Conductance  of  Calcium  Nitrate  in  Acetone  Mixtures  at  0°  at 
V  =  10  and  V  =  1600. 


196        PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

calcium  nitrate  is  obviously  of  the  same  order.  Even  at  a  dilution  of 
1600  liters,  therefore,  calcium  nitrate  is  ionized  less  than  10  per  cent. 
The  addition  of  hydroxy-compounds,  which  tend  to  form  stable  complexes 
with  calcium  salts,  causes  an  enormous  increase  in  the  conductance  of 
solutions  of  this  salt  in  acetone,  even  though  the  amount  of  the  second 
component  added  is  relatively  small.  The  curves  as  drawn  are  only 
rough  approximations  and  it  is  not  improbable  that  the  initial  conduct- 
ance increase  is  even  greater  than  indicated  in  the  figure.  Owing  to  the 
increased  ionization  of  calcium  nitrate  on  the  addition  of  water,  there- 
fore, the  conductance  rises  enormously,  even  though  the  speed  of  the  ions 
is  greatly  depressed  on  the  addition  of  water.  As  a  consequence,  the  con- 
ductance curve  on  addition  of  water  passes  through  a  pronounced  maxi- 
mum at  a  composition  at  or  above  75  per  cent  of  acetone.  On  the 
addition  of  further  amounts  of  water,  the  conductance  curve  follows, 
roughly,  the  fluidity  curve  of  the  solvent  mixture.  The  addition  of 
methyl  alcohol  likewise  results  in  an  increase  in  ionization,  although  this 
increase  is  much  lower  than  in  the  case  of  water.  The  conductance  curve, 
therefore,  passes  through  a  comparatively  flat  maximum  at  a  composition 
in  the  neighborhood  of  25  per  cent  of  acetone.  The  ionization  of  calcium 
nitrate  dissolved  in  a  mixture  of  methyl  alcohol  and  acetone  therefore 
has  not  reached  a  value  corresponding  to  that  of  a  normal  electrolyte, 
even  when  as  much  as  75  per  cent  of  methyl  alcohol  has  been  added. 
The  addition  of  ethyl  alcohol  causes  a  marked  increase  in  the  conductance, 
although  considerably  less  than  that  due  to  methyl  alcohol.  The  curve 
passes  through  a  distinct  maximum,  after  which  the  conductance  de- 
creases, chiefly  owing  to  the  decrease  in  the  fluidity  of  the  mixture. 

At  the  higher  concentration,  the  curves  are  greatly  modified.  Again, 
the  ionization  of  the  electrolyte  is  greatly  increased  on  addition  of  the 
second  solvent,  as  is  indicated  by  a  marked  increase  in  the  conductance 
of  the  solutions.  In  the  case  of  water,  the  curve  exhibits  a  marked  inflec- 
tion point  in  the  neighborhood  of  the  composition  containing  50  per  cent 
of  alcohol  and  water.  At  these  higher  concentrations,  therefore,  solu- 
tions of  calcium  nitrate  in  mixtures  of  acetone  and  water  exhibit  an 
ionization  much  below  that  of  normal  electrolytes.  The  curve,  on  addi- 
tion of  methyl  alcohol,  shows  a  continuous  increase  in  the  conductance 
throughout  its  course.  That  for  ethyl  alcohol  shows  a  slight  increase 
only,  the  curve  exhibiting  a  very  flat  maximum.  At  the  higher  concen- 
trations of  the  salt,  therefore,  the  addition  of  ethyl  alcohol  causes  only 
a  relatively  small  increase  in  the  conductance  of  calcium  nitrate.  Actu- 
ally, however,  the  ionization  is  considerably  increased  on  the  addition  of 
ethyl  alcohol,  since  the  fluidity  of  the  ethyl  alcohol  mixture  is  much  lower 
than  that  of  pure  acetone. 


ELECTROLYTES  IN  MIXED  SOLVENTS  197 

Extensive  data  are  available  which  show  that  the  examples  given 
above  are  typical  of  the  behavior  of  solutions  of  electrolytes  in  mixed 
solvents.  The  data  do  not  have  sufficient  precision  to  make  it  possible 
to  determine  the  values  of  AO  in  the  mixtures,  fof  which  reason  it  is 
necessary  to  consider  only  the  general  outline  of  the  conductance  curves. 
It  is  evident  that,  in  the  case  of  solutions  of  salts  which  are  highly  ionized, 
the  conductance  curves  parallel  the  fluidity  curves.  If,  however,  the 
electrolyte  is  only  slightly  ionized  in  one  of  the  solvents,  the  addition  of 
the  second  component  may  cause  a  large  shift  in  the  conductance  values 
due,  primarily,  to  a  large  change  in  the  ionization  of  the  electrolyte.  It 
should  be  noted  that,  whenever  the  fluidity  of  the  solvent  medium 
changes,  whether  under  the  action  of  pressure  or  temperature,  or  whether 
through  a  change  in  the  viscosity  of  the  medium  due  to  the  presence  of 
the  electrolyte  itself  or  due  to  the  presence  of  a  non-electrolyte,  the  con- 
ductance is  affected  by  the  viscosity  change,  and,  while  the  conductance 
may  not  change  in  direct  proportion  to  the  fluidity  change  of  the  medium, 
nevertheless  the  effect  of  fluidity  change  is  very  marked.  These  facts  are 
in  entire  accord  with  our  notions  as  to  the  nature  of  the  conduction 
process.  On  the  other  hand,  it  is  clearly  evident  that  the  conductance  is 
likewise  dependent  upon  some  other  factor,  namely  the  ionization.  The 
ionization  is  a  function,  in  the  first  place,  of  the  dielectric  constant  of 
the  solvent  medium,  as  well  as  of  the  concentration  of  the  electrolyte. 
In  the  second  place,  however,  the  ionization  is  greatly  affected  by  inter- 
action between  the  dissolved  electrolyte  and  the  solvent  medium.  Ap- 
parently, complexes  are  formed  between  the  dissolved  electrolyte  and  the 
solvent,  which  are  largely  ionized.  Certain  solvents,  such  as  acetone, 
for  example,  appear  to  have  a  very  small  tendency  to  form  complexes. 
When  salts,  which  exhibit  a  marked  tendency  to  form  complexes,  are 
dissolved  in  solvents  of  this  type,  the  resulting  ionization .  is  relatively 
low.  This  effect  is  marked  in  the  case  of  salts  of  the  alkali  metals. 
Salts  of  sodium,  potassium,  rubidium  and  caesium  are  very  largely 
ionized  in  all  solvents,  apparently  without  exception,  whereas  the  salts  of 
lithium  exhibit  a  markedly  lower  ionization  in  many  solvents,  as  for 
example  in  acetone.  As  is  well  known,  lithium  salts  exhibit  a  great 
affinity  for  hydroxy-solvents,  and  apparently  the  formation  of  a  complex 
is  a  necessary  condition  for  ionization  in  the  case  of  salts  of  this  type. 

In  comparing  the  ionizing  power  of  different  solvents,  therefore,  it  is 
necessary  to  select  such  electrolytes  as  exhibit  the  least  tendency  to  form 
complexes.  This  has  in  general  been  done  by  various  writers  on  this 
subject.  Nevertheless,  it  should  be  borne  in  mind  that  the  possibility 
always  exists  that  a  given  electrolyte  in  a  given  solvent  may  exhibit 
exceptional  properties. 


Chapter  VIII. 
Nature  of  the  Carriers  in  Electrolytic  Solutions. 

1.  Interaction  between  the  Ions  and  Polar  Molecules.    The  results 
given  in  the  preceding  chapter  indicate  that  an  equilibrium  exists  between 
the  ions,  and  possibly  the  un-ionized  fraction,  of  a  dissolved  electrolyte 
and  the  molecules  of  an  added  non-electrolyte  of  the  polar  type.    If 
reactions  of  this  type  take  place  between  a  non-electrolyte  and  an  elec- 
trolyte, both  of  which  are  present  in  relatively  small  amounts  in  the 
solvent  medium,  then  there  is  all  the  more  reason  for  believing  that 
reaction  takes  place  between  the  electrolyte  and  the  non-electrolyte  when 
the  latter  is  present  in  large  excess.    Apparently,  the  ions  in  solution  do 
not  consist  merely  of  the  charged  groups  present  in  the  original  salt, 
but  rather  of  these  groups  associated  with  the  solvent.    Where  the  ions 
possess  great  tendency  to  form  definite  complexes  with  the  solvent,  as  is 
the  case,  for  example,  with  the  calcium  ion  in  water  and  the  silver  ion  in 
ammonia,  a  portion  of  the  solvent  is  present  in  the  form  of  a  definite 
chemical  compound.     In  addition  to  this,  however,  an  ion  may  con- 
ceivably be  associated  with  a  further  amount  of  solvent  as  a  result  of  the 
charge  on  the  ion  and  the  electrical  moment  of  the  solvent  molecules. 

2.  Hydration  of  the  Ions  in  Aqueous  Solution.     It  has  been  defi- 
nitely established  that  in  aqueous  solutions  certain  ions  are  hydrated ; * 
that  is,  in  passing  through  the  solution  they  carry  water  with  them. 
Since  the  conductance  values  of  all  ions  in  water  are  of  the  same  general 
order  of  magnitude,  it  follows  that  all  ions  are  in  all  likelihood  hydrated, 
save,  perhaps,  the  highly  complex  ions. 

If  the  ions  are  hydrated,  then,  in  the  course  of  a  transference  experi- 
ment, water  will  be  transferred  toward  one  electrode  or  the  other.    If 

N^  represents  the  number  of  molecules  of  water  associated  with  the 
anion  and  N  the  number  of  molecules  of  water  associated  with  the 
cation  and  if  T  is  the  fraction  of  the  current  carried  by  the  anion,  that 


1Lobry  de  Bruyn,  Rec.  Trav.  Ohim.  22,  430  (1903)  ;  Morgan  and  Kanolt,  J.  Am  Chem 
800.  28,  572  (1906)  ;  Bucbbock,  Ztachr.  f.  phtfs.  Chem.  55,  563  (1906)  ;  Washburn,  J  Am 
Chem.  Soc.  31,  322  (1909)  ;  Washburn  and  Millard,  J.  Am.  Chem.  /S'oc.  37,  694  (1915). 

198 


CARRIERS  IN  ELECTROLYTIC  SOLUTIONS  199 

is,  if  this  is  the  true  transference  number  of  the  anion,  and  if  T^  is  the 

true  transference  number  of  the  cation,  then  according  to  Washburn 2 
the  net  transfer  of  water  per  equivalent  of  electricity  passing  through 
the  solution  will  be: 


(47) 

V  IA/  V  14/  <A/ 

where  JV     is  the  net  transfer  of  water  per  equivalent  of  electricity. 
In  general,  therefore,  the  passage  of  a  current  through  a  solution  will 

E» 

be  accompanied  by  a  net  transfer  of  water,  whose  value  is  N     per 

equivalent  of  electricity.  This  transfer  of  water  may  be  determined  by 
introducing  into  the  solution  a  substance  which  itself  takes  no  part  in 
the  transfer  of  the  charge.  The  change  in  the  concentration  of  the  water 
with  respect  to  this  reference  substance  will  give  the  transfer  of  water, 
and  the  change  in  the  concentration  of  the  salt  with  respect  to  the  same 
reference  substance  will  give  the  true  transference  number  of  the  salt  at 
the  same  time.  It  follows,  therefore,  that  if  the  true  transference  num- 
ber of  the  salt  and  the  net  transference  number  of  the  water  are  known, 
the  relative  amounts  of  water  associated  with  the  two  ions  may  be  deter- 
mined. As  ordinarily  carried  out,  transference  experiments  in  which 
water  is  employed  as  reference  substance  yield,  not  the  true  transference 
number,  but  a  transference  number  differing  therefrom  by  an  amount 
depending  upon  the  relative  amount  of  water  transferred.  The  relation 
between  the  true  and  the  ordinary  transference  number  is  given  by  the 
equation: 

(48) 

N 

where  T^   is  the  ordinary  transference  number  of  the  cation  and   -^ 

w 

is  the  ratio  of  the  number  of  mols  of  salt  to  that  of  water  in  the  solution. 
If  transference  measurements  on  various  electrolytes  with  a  common  ion 
are  carried  out,  then  the  relative  hydration  of  the  uncommon  ions  may 
be  determined.  The  absolute  hydration  of  the  ions  is  of  course  not 
determinable.  In  Table  LXXX  are  given  values  of  the  true  transference 
number,  the  ordinary  transference  number,  and  the  water  transference 

•  Washburn,  Joe.  ait. 


200        PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

number  for  different  electrolytes  in  water  at  a   concentration  of   1.2 
normal  at  25°. 

TABLE   LXXX. 

TRANSFERENCE  NUMBERS  OP  ELECTROLYTES  AND  SOLVENT  FOR 
AQUEOUS  SOLUTIONS. 

HC1         CsCl        KC1         NaCl         LiCl 

5Pf     ............     0.844        0.491        0.495        0.383        0.304 

I 

TCQ     ............     0.820        0.485        0.482        0.366        0.278 


0.24          0.33          0.60          0.76          1.5 


In  solutions  of  these  electrolytes,  the  net  transfer  of  water  takes 
place  from  the  anode  to  the  cathode,  as  shown  by  the  values  given  in  the 

W 

table  for  N   .    In  these  cases,  correspondingly,  the  true  transference 

numbers  of  the  cations  are  larger  than  the  ordinary  transference  num- 
bers. It  is  obvious  from  Equation  48  that,  as  the  concentration  of  the 
solution  decreases,  the  ordinary  transference  number  approaches  the 
true  transference  number.  The  relation  between  the  water  carried  by 
the  cation  and  that  by  the  chloride  ion  is  evidently  given  by  the  fol- 
lowing equations: 

N^   =0.28  +  1.085^, 


(49)  N*   =1.3   +1.02    N™, 


=  0.67  +  1.03    N, 
=1.3   +1.02 
=2.0   +1.61 


Nwl  =*-7   +2'29    N°1'        '  ' 

Since  the  hydration  of  the  chloride  ion  is  not  known,  the  absolute  hydra- 
tion  of  the  various  cations  may  not  be  determined.  If,  however,  a  value 
is  assumed  for  the  hydration  of  the  chloride  ion,  then  the  hydration  of  the 
other  ions  may  at  once  be  calculated  by  means  of  these  equations.  The 
values  of  the  hydration  of  the  different  cations  for  different  assumed 
values  for  the  hydration  of  the  chloride  ion  are  given  in  the  following 
table: 


CARRIERS  IN  ELECTROLYTIC  SOLUTIONS  201 

TABLE  LXXXI. 

CALCULATED  HYDRATION  OF  THE  IONS  FOR  DIFFERENT  ASSUMED  VALUES 
FOR  THE  HYDRATION  OF  THE  CHLORIDE  ION. 

NCl  N-H.  NCs  NK  ^Na  ^Li 

w  w  w  www 

0  0.28  0.67  1.3  2.0  4.7 

4  1.0  4.7  5.4  8.4  14. 

9  2.0  9.9  10.5  16.6  25.3 

The  assumption  that  the  chloride  ion  is  un-hydrated  is  improbable, 
since  the  conductance  of  the  chloride  ion  is  very  nearly  equal  to  that  of 
the  potassium  ion.  The  value  assumed  for  the  hydration  of  the  chloride 
ion  should  therefore  differ  little  from  that  of  the  potassium  ion.  This 
necessitates  assuming  for  the  chloride  ion  a  value  not  materially  less 
than  4.  In  all  likelihood  the  true  value  lies  somewhere  between  3  and  9, 
although  the  true  value  must  necessarily  remain  uncertain.  Below  are 
given  the  values  of  the  ionic  conductance  for  the  different  ions  at  18°, 
together  with  the  ratio  of  these  conductances  to  that  of  the  hydrogen  ion. 

TABLE  LXXXII. 
COMPARISON  OF  IONIC  CONDUCTANCES  AND  HYDRATION  NUMBERS. 

xrCl        xrH         ArCs        xr-K-        xr-Na        AT  Li 
1\  I\  I\  IV  xv  iV          • 

w  w  w  w  w  w 

Hydration  No 4.0  1.0          4.7          5.4          8.4        14.0 

Ionic  Cond 65.5        315.          68.0        64.5        43.4        33.3 

315/A     4.8  1.0          4.6          4.9          7.3          9.5 

It  is  seen  that  the  values  of  the  ionic  conductances  relative  to  that 
of  the  hydrogen  ion  correspond  roughly  with  the  values  of  the  hydration 
of  the  different  ions,  assuming  the  hydration  of  the  hydrogen  ions  to  be 
unity.  An  exact  correspondence  between  the  hydration  and  the  con- 
ductance is  not  to  be  expected.  Nevertheless,  except  in  the  case  of  the 
caesium  and  the  chloride  ions,  the  order  of  the  reciprocal  conductance 
values  corresponds  with  the  order  of  the  hydration  numbers.  The 
chloride,  caesium,  and  potassium  ions  are  among  the  most  rapidly  mov- 
ing ions  in  water,  excepting  the  hydrogen  and  hydroxyl  ions,  and  it  may 
therefore  be  concluded  that  all  ions  in  water  are  hydrated  at  least  as 
much  as  the  chloride  ion.  It  is  possible,  of  course,  that  the  hydration 
numbers  may  be  considerably  larger  than  those  assumed  on  the  basis 
of  an  hydration  of  4  for  the  chloride  ion.  How  the  hydration  of  the  ions 


202        PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

varies  with  the  temperature  and  the  concentration  is  not  known.  If 
the  absolute  hydration  of  the  ions  is  large,  then  it  is  to  be  expected  that 
the  hydration  will  change  at  higher  concentrations.  It  is  possible, 
therefore,  that  at  concentrations  below  1.2  normal  the  hydration  of  the 
ions  may  be  considerably  greater  than  at  the  higher  concentration. 

As  we  have  seen  in  an  earlier  section,  at  higher  temperatures  the 
conductance  of  the  more  rapidly  moving  ions  approaches  that  of  the 
more  slowly  moving  ions.  At  the  same  time,  as  we  have  seen,  the  con- 
ductance of  the  more  slowly  moving  ions  changes  almost  in  exact  pro- 
portion to  the  fluidity  change  of  the  solvent.  It  may  be  concluded, 
therefore,  that,  at  higher  temperatures,  the  hydration  of  the  more  rapidly 
moving  ions  increases  and  approaches  that  of  the  more  slowly  moving 
ions,  such  as  that  of  the  lithium  ion.  It  is  probable,  therefore,  that  as 
the  temperature  increases  the  net  transference  of  water  diminishes,  while 
the  absolute  amount  of  water  associated  with  the  ions  increases. 

3.  Calculation  of  Ion  Dimensions  from  Conductance  Data.  Lorenz2a 
has  calculated  the  ion  dimensions  from  the  ion  conductances,  by  means 
of  the  Einstein-Stokes 2b  equation.  The  values  obtained  for  the  ion 
dimensions  have  been  compared  with  those  obtained  by  other  methods, 
as  determined  from  the  density  of  substances  in  a  condensed  state,  assum- 
ing close  packing  of  the  molecules.  For  ions  containing  a  large  number 
of  atoms,  particularly  large  organic  anions  and  cations,  the  calculated 
values  from  the  conductance  data  agree  well  with  those  derived  by  other 
methods.  In  the  case  of  the  simpler  ions,  however,  a  similar  agreement 
has  not  been  found.  In  the  case  of  the  alkali  metals,  for  example, 
lithium,  which  has  the  smallest  atomic  volume,  has  the  lowest  conduct- 
ance, while  caesium,  with  the  largest  atomic  volume,  has  the  highest 
conductance.  It  has  generally  been  assumed  that  the  reversal  in  the 
order  of  the  conductance  of  the  ions  of  the  alkali  metals  is  due  to 
hydration. 

Born 2C  and  Lorenz  2d  consider  that  the  Einstein-Stokes  equation  is 
applicable  even  in  the  case  of  small  ions  and  that  the  observed  diverg- 
ence is  due  to  electrical  interaction  between  the  charge  on  the  ions  and 
the  adjacent  solvent  molecules.  This  electromagnetic  frictional  effect 
is  the  greater,  the  smaller  the  volume  of  the  ion.  The  total  frictional 
effect  which  the  ion  experiences  is  thus  the  sum  of  two  effects,  one  of 
which  decreases  and  the  other  of  which  increases  with  decreasing  ionic 
diameter.  The  function  which  expresses  the  ionic  resistance  in  terms 

2a  Lorenz,  Ztschr.  /.  Elektroch.  26,  424   (1920)  ;  Ztschr.  f.  pliys.  Chem.  73,  252   (1910)  ; 
also,  numerous  articles  in  the  Ztachr.  f.  Anory.  Chem. 
ab  Einstein,  Ann.  d.  Phys.  11,  549   (1905). 
acBorn,  Ztschr.  f.  Elektroch.  26,  401   (1920). 
2d  Lorenz,  loc.  cit. 


CARRIERS  IN  ELECTROLYTIC  SOLUTIONS  203 

of  the  ionic  diameter  therefore  passes  through  a  minimum.  In  this  way 
Born  accounts  for  the  diminishing  values  of  the  ion  conductance  with 
decreasing  volume  in  the  case  of  the  simpler  ions. 

The  constants  involved  in  the  equation  for  the  electro-frictional  effect 
are  somewhat  uncertain.  In  any  case,  these  constants  should  depend 
solely  upon  the  properties  of  the  solvent  medium,  assuming  an  ion  of 
fixed  dimensions. 

The  correctness  of  this  theory  appears  somewhat  doubtful.  In  the 
first  place,  it  is  difficult  to  account  for  the  fact  that  at  higher  tempera- 
tures the  ion  conductances' in  aqueous  solutions  approach  the  same  value. 
While  it  is  true  that  the  dielectric  constant  of  the  medium  varies  with 
the  temperature,  an  effect  of  the  order  of  that  observed  in  aqueous  solu- 
tions is  scarcely  to  be  expected.  More  convincing,  perhaps,  is  the  rela- 
tion of  the  ion  conductances  in  non-aqueous  solutions.  If  the  theory  of 
Born  and  Lorenz  is  correct,  the  order  of  the  ion  conductances  should  be 
the  same  in  different  solvents.  This  is  by  no  means  the  case.  For  exam- 
ple, as  may  be  seen  from  the  values  of  the  ion  conductances  in  liquid 
ammonia  given  in  an  earlier  chapter,  the  conductance  of  the  silver  ion 
is  markedly  lower  than  that  of  the  sodium  ion  in  ammonia;  while  in 
water  the  conductance  of  the  sodium  ion  is  much  smaller  than  that  of  the 
silver  ion.  Again,  the  conductance  of  the  ammonium  ion  in  ammonia  is 
practically  identical  with  that  of  the  sodium  ion,  whereas  the  conduct- 
ance of  the  ammonium  ion  in  water  is  almost  identical  with  that  of  the 
potassium  ion.  While  the  conductance  of  the  lithium  ion  in  water  is 
much  smaller  than  that  of  the  silver  ion,  the  conductance  of  the  lithium 
ion  in  ammonia  differs  but  little  from  that  of  the  silver  ion.  So,  also, 
in  the  case  of  anions,  the  conductance  of  the  nitrate  ion  is  identical  with 
that  of  the  iodide  ion  in  ammonia,  while  in  water  it  is  much  smaller. 
Similarly,  the  conductance  of  the  chloride  ion  in  ammonia  is  markedly 
greater  than  that  of  the  iodide  ion;  whereas  in  water  the  conductance  of 
the  iodide  ion  is  greater  than  that  of  the  chloride  ion.  An  examination 
of  the  conductance  values  of  electrolytes  in  other  non-aqueous  solvents 
shows  that  here,  too,  the  order  of  ion  conductances  is  a  characteristic 
property  of  the  solvent  medium  and  of  the  dissolved  electrolytes.  For 
example,  in  acetone  the  conductance  values  of  the  lithium,  sodium  and 
potassium  ions  are  practically  identical;  while  the  conductance  of  the 
ammonium  ion  is  markedly  greater  than  that  of  the  potassium  ion. 
While  in  water  the  conductance  of  the  sulphocyanate  ion  is  markedly 
lower  than  that  of  the  iodide  ion,  in  acetone  the  conductance  of  this  ion 
is  greater  than  that  of  the  iodide  ion.  So,  also,  in  pyridine  the  con- 


204        PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

ductance  of  the  sulphocyanate  ion  is  markedly  greater  than  that  of  the 
iodide  ion. 

It  is  evident  that,  applied  to  solutions  in  non-aqueous  solvents,  the 
theory  of  Born  and  Lorenz  meets  with  great  difficulties.  The  values  of 
the  ion  conductances  in  different  solvents  are  in  much  better  agreement 
with  the  assumption  that  the  differences  in  the  ion  velocities  of  the 
simpler  ions  are  primarily  due  to  the  size  and  nature  of  the  complexes 
formed  between  the  ion  and  the  solvent  medium.  An  ion  will,  in  gen- 
eral, exhibit  a  low  conductance  in  a  medium  with  which  it  has  a  great 
tendency  to  form  stable  complexes.  On  the  other  hand,  in  media  with 
which  the  tendency  to  form  complexes  is  less  pronounced,  its  conductance 
will  be  relatively  high.  Thus,  the  silver  and  ammonium  ions  in  ammonia 
have  a  relatively  low  conductance;  while  in  acetone,  sodium  and  lithium 
have  a  relatively  high  conductance.  The  properties  of  solutions  of  these 
salts  in  the  solvents  mentioned  indicate  a  high  solvation  in  ammonia 
solutions  and  a  low  solvation  in  acetone  solutions. 

It  has  been  demonstrated  by  means  of  transference  measurements  in 
aqueous  solutions  that  the  alkali  metal  and  hydrogen  ions  are  hydrated. 
While  the  absolute  degree  of  hydration  remains  uncertain,  it  is  probably 
safe  to  assume  that  the  hydration  of  the  hydrogen  ion  is  not  less  than 
unity,  which  requires  a  hydration  in  the  neighborhood  of  5  for  the 
potassium  ion  and  14  for  the  lithium  ion. 

As  we  have  seen  in  Chapter  V,  the  relation  between  the  conductance, 
i.e.,  the  speed  of  an  ion,  and  the  viscosity  of  the  medium  through  which 
it  moves  is  anything  but  simple.  The  conductance  of  ions  of  small 
dimensions  is  not  proportional  to  the  fluidity  of  the  ionizing  solvent. 
On  the  addition  of  a  second  non-ionic  component,  the  conductance  change 
of  the  ion  is  approximately  proportional  to  the  fluidity  change  of  the 
medium  only  when  the  molecules  of  the  added  substance  are  small. 
When  the  dimensions  of  the  molecules  of  the  added  substance  are  large 
compared  with  those  of  the  ions,  the  conductance  change  is  invariably 
smaller  than  the  fluidity  change. 

Finally,  Dummer  2e  has  measured  the  diffusion  coefficients  of  a  num- 
ber of  organic  solvents  of  varying  molecular  volume  in  one  another  and 
compared  his  results  with  one  another  by  means  of  the  Einstein-Stokes 
equation.  The  molecular  dimensions  found  for  the  same  substance  in 
different  solvents  do  not  agree  well  with  one  another.  The  Einstein- 
Stokes  equation  should  be  applied  with  caution  to  systems  of  particles 
of  molecular  dimensions. 

»•  Dummer ,Ztschr.  f.  anorg.  Ohem.  109,  31  (1919).  Compare  also,  oholm,  Medd  K 
Vetens-Akad's  Nobehnstitut,  Nos.  23,  24  and  26  (1912). 


CARRIERS  IN  ELECTROLYTIC  SOLUTIONS  205 

4.  The  Hydrogen  and  Hydroxyl  Ions.  In  aqueous  solutions,  the 
hydrogen  and  hydroxyl  ions  appear  to  occupy  a  more  or  less  unique 
position.  They  are  characterized  by  the  exceptionally  high  value  of  their 
ionic  conductance.  At  0°,  the  hydrogen  ion  moves  approximately  10 
times  as  fast  as  the  acetate  ion,  or  approximately  5  times  as  fast  as  the 
potassium  ion.  At  the  same  temperature  the  hydroxyl  ion  moves  from 
5  to  6  times  as  fast  as  the  acetate  ion.  The  question  as  to  the  cause  of 
the  high  values  for  the  conductance  of  these  two  ions  in  water  naturally 
arises.  A  more  or  less  obvious  explanation  is:  that  these  ions  are 
hydrated  to  a  much  smaller  extent  than  are  the  other  ions;  or,  in  other 
words,  they  are  relatively  smaller  than  the  other  ions.  This  view,  more- 
over, is  supported  by  the  results  obtained  from  transference  experiments. 
As  was  shown  in  the  preceding  section,  the  amount  of  water  associated 
with  the  hydrogen  ion  is  much  smaller  than  that  associated  with  any 
other  positive  ion  for  which  data  exist.  It  might  be  expected,  therefore, 
that  the  speed  of  the  hydrogen  ion  would  have  an  abnormally  high  value 
because  of  its  low  hydration.  Presumably,  a  similar  explanation  would 
hold  in  the  case  of  the  hydroxyl  ion,  although  here  we  have  no  data  as 
to  the  relative  hydration.  That  the  hydrogen  ion  is  in  fact  hydrated, 
admits  of  no  question.  The  minimum  amount  of  water  which  might  be 
associated  with  the  hydrogen  ion  is  0.28  mol.  It  is  improbable,  how- 
ever, that  hydrogen  ions  exist  in  water  unassociated  with  water  molecules. 
In  an  earlier  section  it  was  shown  that  the  addition  of  water  to  alcohol 
solutions  of  the  strong  acids  greatly  diminishes  the  conductance  of  the 
acid,  while  the  addition  of  water  to  a  solution  of  a  weak  acid  greatly 
increases  the  conductance  of  the  acid.  It  may  be  inferred  from  this  that 
a  complex  is  formed  between  the  hydrogen  ion  and  the  added  water  whose 
speed  is  much  lower  than  that  of  the  normal  hydrogen  ion  in  alcohol. 
In  the  case  of  the  weak  acids,  the  addition  of  water  increases  the  ioniza- 
tion,  owing  to  the  formation  of  a  complex  between  water  and  the  acid. 

The  formation  of  a  more  or  less  definite  complex  between  an  acid 
and  water  is  moreover  indicated  by  the  large  energy  change  accompany- 
ing the  solution  of  acids  in  water.  It  has  been  suggested  that  the  hydro- 
gen ion  is  indeed  an  oxonium  ion,  bearing  the  same  relation  to  oxygen 
that  the  ammonium  ion  does  to  nitrogen.  The  hydrogen  ion  would  there- 
fore be  OH3+.  That  the  oxygen  compounds  form  salt-like  substances 
with  the  halogen  acids  is  further  borne  out  by  the  fact  that  oxygen  com- 
pounds dissolved  in  the  liquid  halogen  acids  almost  invariably  yield 
electrolytic  solutions,  some  of  which  are  ionized  almost  as  much  as  the 
typical  salts.3  At  the  same  time  it  has  been  shown  that  the  organic 

'Archibald,  Journal  de  Chlmie  Physique,  n,  741    (1913). 


206        PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

substance  is  associated  with  the  cation.4  In  the  case  of  sulphur,  which 
element  is  closely  related  to  oxygen,  salts  of  the  type  R3SX  are  well 
known. 

Correspondingly,  the  ammonium  salts  dissolved  in  liquid  ammonia 
exhibit  all  the  properties  of  acids,  and  the  ammonium  ion  exhibits  the 
properties  characteristic  of  the  hydrogen  ion.5  If  this  conception  regard- 
ing the  nature  of  the  hydrogen  ion  is  correct,  we  should  expect  solutions 
of  the  acids  in  solvents,  which  do  not  possess  the  power  of  forming  com- 
plexes of  the  type  R30+,  to  be  relatively  poor  conductors.  Such  indeed 
appears  to  be  the  case.  Dissolved  in  the  alcohols,  hydrogen  chloride 
conducts  fairly  well;  while  dissolved  in  acetone,6  hydrogen  chloride 
yields  a  solution  of  very  low  conducting  power.  In  view  of  the  fairly 
high  dielectric  constant  of  acetone,  it  is  difficult  to  account  for  this  be- 
havior of  the  acid  except  on  the  assumption  that  in  this  case  there  is 
little  tendency  to  form  the  oxonium  complex.  There  are  no  data  to  indi- 
cate that  hydrogen  chloride  is  a  conductor  when  dissolved  in  sulphur 
dioxide  or  any  other  solvent  which  does  not  contain  oxygen,  nitrogen  or 
other  atoms  capable  of  forming  complexes. 

These  various  facts  indicate  that  the  hydrogen  ion  in  water  is,  in 
fact,  not  a  hydrogen  ion,  but  an  oxonium  ion.  Whether  the  charge  is 
associated  with  the  hydrogen  or  with  the  oxygen  atom  cannot  be  deter- 
mined in  this  case  any  more  than  it  can  in  that  of  the  similar  ammonium 
salts.  It  appears  likely,  however,  that  in  salts  of  this  type  the  charge 
is  associated  either  with  the  oxygen  or  nitrogen  atom,  or  with  the  group 
as  a  whole,  rather  than  with  one  of  the  hydrogen  atoms. 

5.  Ions  of  Abnormally  High  Conductance.  Certain  writers  have 
sought  to  relate  the  abnormally  high  conductance  of  the  hydrogen  and 
hydroxyl  ions  with  the  fact  that  these  ions  are  products  of  the  ionization 
of  the  solvent  itself.7  They  have  therefore  adopted  a  theory  founded 
upon  the  old  theory  of  Grotthuss,8  according  to  which  the  mechanism  of 
the  conduction  process  consists,  not  in  a  transfer  of  the  ions  through  the 
solution,  but  in  an  ordered  arrangement  of  the  polar  molecules  of  the 
electrolyte,  alternately  positive  and  negative,  in  accordance  with  the  im- 
pressed field.  An  interchange  of  positive  and  negative  carriers  takes 
place  between  adjacent  molecules  resulting  thus  in  a  separation  of  the 
products  at  the  two  electrodes.  The  work  of  Faraday  and  Hittorf  has 
definitely  overthrown  the  theory  of  Grotthuss,  but  these  later  writers 

'Steele,  Mclntosh  and  Archibald,  Ztschr.  f.  phys.  Chem.  55,  176   (1906). 

'Franklin  and  Kraus,  Am.  Chem.  J.  23,  304  (1900);  Franklin  and  Stafford,  Am. 
Chem.  J.  28,  83  (1902)  ;  Franklin,  Am.  Chem.  J.  Jft,  285  (1912). 

6Lucasse,  Thesis,  Clark  Univ.,  1920. 

TDanneel,  Ztschr.  f.  Electroch.  11,  249  (1905)  ;  Hantzsch  and  Caldwell,  Ztschr.  f. 
phys.  Chem.  58,  575  (1907). 

8  Ann.  d.  Chim.  58,  54  (1806). 


CARRIERS  IN  ELECTROLYTIC  SOLUTIONS  207 

assume  that,  in  the  case  of  the  hydrogen  and  the  hydroxyl  ions  in  water, 
an  interchange  takes  place  between  the  ions  and  the  solvent  molecules 
with  the  result  that  the  mean  path  over  which  these  ions  travel  is  reduced 
in  proportion  to  the  effective  diameter  of  the  solvent  molecules  which  are 
concerned  in  the  interchange.  A  priori,  there  is  nothing  to  indicate  that 
this  hypothesis  may  not  be  correct.  If  it  is  correct,  however,  it  must 
lead  to  certain  definite  consequences  which  we  may  now  examine. 

In  the  first  place,  it  is  to  be  expected  that  a  similar  phenomenon  will 
be  found  in  solutions  in  non-aqueous  solvents  which  are  capable  of 
furnishing  ions.  In  the  case  of  liquid  ammonia  an  equilibrium.  exists  of 
the  type: 


or,  perhaps, 

2NH3  =  NH2- 

where  NH4+  is  the  ammonium  ion  and  NH2"  is  the  basic  ion  of  liquid 
ammonia.  That  such  an  equilibrium  exists,  is  indicated  by  the  fact  that 
certain  ammonolytic  equilibria  exist  in  ammonia  solutions  comparable  in 
all  respects  with  hydrolytic  equilibria  in  aqueous  solutions.9  On  the 
basis  of  the  above  hypothesis,  we  should  expect  that  the  ammonium  ions 
and  the  NH2~  ions  would  exhibit  an  exceptionally  high  conducting  power 
in  liquid  ammonia  solutions.  As  may  be  seen  by  referring  to  the  table 
of  ionic  conductances  in  Chapter  II,  the  amide  ion  in  liquid  ammonia 
possesses  a  conducting  power  markedly  lower  than  that  of  typical  nega- 
tive ions,  while  the  conductance  of  the  ammonium  ion  is  distinctly  lower 
than  that  of  the  potassium  ion.  It  follows,  therefore,  that  in  ammonia 
solutions  the  ammonium  and  the  amide  ions  are  in  no  wise  exceptional. 
It  has  been  maintained  that  the  conductance  of  the  alcoholate  ion  in  the 
alcohols  is  abnormally  high.  According  to  the  best  data  available,  how- 
ever, the  conductance  of  the  alcoholates  in  alcohol  10  is  of  the  same  order 
as  that  of  typical  salts  in  these  solvents. 

As  a  result  of  conductance  and  transference  measurements  with  the 
formates  in  formic  acid  it  has  been  shown  that  the  formate  ion  in  formic 
acid  possesses  an  exceptionally  high  conducting  power.  While  the  pre- 
cise values  are  somewhat  uncertain,  roughly,  the  ionic  conductances  of 
the  sodium,  potassium  and  formate  ions  in  formic  acid  at  25°  are  14.6, 
17.5  and  51.  6.11  The  limiting  value  of  the  conductance  of  hydrochloric 
acid  in  formic  acid  is  approximately  75,  compared  with  the  value  69.4  12 

•Franklin,  J.  Am.  Chem.  Soc.  27,  820   (1905). 

"Robertson  and  Acree,  Intern.  Congr.  Appd.  Chem.   [8]  26,  609   (1912). 

11  Schlesinger  and  Bunting,  J.  Am.  Chem.  Soc.  41,  1934   (1919). 

»  Schlesinger  and  Martin,  J.  Am.  Chem.  Soc.  36,  1618   (1914). 


208        PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

for  potassium  formate,  for  example.  Since  the  transference  number  of 
hydrochloric  acid  in  formic  acid  is  not  known,  it  is  uncertain  whether 
or  not  the  hydrogen  ion  in  formic  acid  possesses  an  abnormally  high 
conducting  power.  The  evidence,  however,  indicates  that  the  chloride 
ion  possesses  a  conducting  power  not  greatly  smaller  than  that  of  the 
formate  or  hydrogen  ion.  The  limiting  value  of  the  conductance  of 
ammonium  chloride  can  scarcely  be  lower  than  52.13  The  value  is  some- 
what uncertain  because  of  the  solvolytic  reaction  between  the  salt  and 
the  solvent.  However,  assuming  probable  values  for  the  ionization  con- 
stants of  ammonium  formate  and  hydrochloric  acid  and  pure  formic  acid, 
it  can  be  shown  that  the  fraction  of  salt  transformed  to  acid  and  base 
by  reaction  with  the  solvent  cannot  affect  the  conductance  by  more  than 
a  few  units.  If  we  assume,  therefore,  the  value  52  for  the  limiting  value 
of  the  equivalent  conductance  of  ammonium  chloride,  and  assuming  for 
the  conductance  of  the  ammonium  ion  the  value  18.8,  which  follows  from 
the  value  70.4  for  the  limiting  value  of  the  equivalent  conductance  of 
ammonium  formate,  we  obtain  for  the  limiting  value  of  the  conductance 
of  the  chloride  ion  the  value  33.2  and  for  the  hydrogen  ion  42.8.  This 
indicates  that  the  conductance  of  the  hydrogen  ion  in  formic  acid  does 
not  differ  greatly  from  that  of  the  chloride  ion  in  the  same  solvent.  The 
exceptionally  high  value  found  for  the  conductance  of  the  hydrogen  and 
the  formate  ions,  like  that  of  the  chloride  ion,  is  presumably  due  to  the 
relatively  smaller  dimensions  of  these  ions  compared  with  those  of  the 
positive  ions  in  formic  acid. 

It  has  also  been  suggested  that  the  pyridonium  ion,  C6H5NH+,  pos- 
sesses an  abnormally  high  conducting  power  in  pyridine.14  This,  how- 
ever, rests  upon  a  false  accepted  value  for  the  conductance  of  typical 
salts  in  pyridine.  The  conductance  of  pyridine  hydrochloride  at  a  dilu- 
tion of  32  liters  and  25°  in  pyridine  has  been  found  to  be  27.4.  The 
conductance  of  sodium  iodide  in  pyridine  at  a  dilution  of  57.7  liters  and 
18°  is  23.6.15  In  general,  at  these  concentrations,  the  conductance  of 
solutions  in  pyridine  changes  but  little  with  concentration.  Conse- 
quently the  conductance  of  sodium  iodide  in  pyridine  at  32  liters  would 
differ  but  little  from  that  at  the  lower  concentration.  On  the  other  hand, 
the  conductance  at  18°  is  materially  lower  than  at  25°  because  of  the 
greater  viscosity  of  the  solution  at  the  lower  temperature.  Assuming  a 
viscosity  correction  of  two  per  cent  per  degree  the  conductance  of  sodium 
iodide  at  25°  would  be  approximately  27.0.  In  other  words,  the  con- 

"Schlesinger  and  Calvert,  J.  Am.  Chem.  Soc.  33,  1924   (1911). 

14  Hantzsch  and  Caldwell,  loo.  cit. 

15  Ottiker,  Dissertation,  Lausanne    (1907);    Kraus    and    Bray,    J.    Am.    Chem.    Soc.    35, 
1379   (1913). 


CARRIERS  IN  ELECTROLYTIC  SOLUTIONS  209 

ductance  of  a  typical  salt  in  pyridine  differs  but  little  from  that  of  a 
salt  of  the  solvent  itself. 

While,  therefore,  there  are  cases  in  which  the  ions  common  to  the 
solvent  exhibit  an  abnormally  high  conducting  power,  as  they  do  in 
water  at  ordinary  temperatures,  there  are  other  cases  in  which  the  con- 
ducting power  of  these  ions  is  entirely  normal.  In  this  connection  it  is 
to  be  borne  in  mind  that  with  rising  temperature  the  speed  of  the  hydro- 
gen and  hydroxyl  ions  in  water  approaches  that  of  the  more  slowly 
moving  ions.  At  306°  the  conductance  of  the  hydrogen  ion  differs  from 
that  of  the  potassium  ion  less  than  the  conductance  of  the  potassium  ion 
differs  from  that  of  the  acetate  ion  at  ordinary  temperatures.  As  has 
been  pointed  out,  the  relative  decrease  in  the  speed  of  the  more  rapidly 
moving  ions  at  higher  temperatures  is  due  to  the  increase  in  the  size 
of  the  more  rapidly  moving  ions.  It  seems  more  rational,  therefore,  to 
ascribe  the  abnormally  high  speed  of  the  hydrogen  and  hydroxyl  ions  in 
water  to  the  low  value  of  their  hydration,  which  moreover  is  in  accord 
with  the  experimentally  determined  values  of  the  relative  hydration  of 
the  different  ions  in  water  at  ordinary  temperatures. 

While  it  cannot  be  definitely  stated  that  all  hydrogen  ions  in  water 
are  associated  with  at  least  one  molecule  of  water,  it  nevertheless  appears 
probable  that  such  is  the  case.  Were  the  hydrogen  ion  unhydrated,  we 
should  expect  a  much  greater  value  for  the  conductance  of  the  hydrogen 
ion.  In  the  case  of  liquid  ammonia  solutions,  it  has  been  shown  that  the 
speed  of  the  negative  electron,  which  at  low  concentrations  is  associated 
with  at  least  one  ammonia  molecule,  is  approximately  seven  times  that  of 
the  sodium  ion.  It  seems  not  unlikely  that  the  negative  electron  in  dilute 
solutions  is  actually  associated  with  a  greater  number  of  ammonia  mole- 
cules. Taking  all  these  facts  into  consideration,  it  appears  probable  that 
the  hydrogen  ion  is  associated  with  at  least  one  molecule  of  water. 

It  is  evident  that  our  conception  as  to  the  nature  of  the  ions  has 
undergone  a  great  amplification  during  the  past  twenty  years.  Prior  to 
that  time  the  ion  of  an  element  was  looked  upon  merely  as  an  atom  of 
the  element  associated  with  a  charge.  Now,  however,  we  know  that  the 
ions  consist  of  more  or  less  definite  complexes  containing  the  solvent,  and 
the  nature  and  dimensions  of  these  complexes  depend,  not  alone  upon 
the  properties  of  the  electrolyte  and  of  the  solvent,  but  also  upon  the 
condition  under  which  the  solution  exists,  such  as  concentration,  tempera- 
ture, pressure,  etc. 

6.  The  Complex  Metal- Ammonia  Salts.  A  number  of  salts  of  the 
heavy  metals,  particularly  those  of  cobalt,  chromium  and  the  platinum 
metals,  form  series  of  compounds  with  ammonia  in  which  there  appears 


210        PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

a  remarkable  relationship  between  the  number  of  ammonia  molecules 
associated  with  the  complex  salt  and  the  properties  of  the  salt,  both  in 
solution  and  in  a  crystalline  state.  While  the  compounds  containing 
ammonia,  or  ammonia  derivatives,  are,  in  general,  the  most  stable  repre- 
sentatives of  this  class,  many  other  compounds  are  known  where  other 
molecules  function  in  a  manner  similar  to  those  of  ammonia.  These 
complex  salts  have  been  studied  extensively  by  a  number  of  investigators, 
notably  by  Werner,16  who  has  proposed  a  theory  of  the  constitution  of 
these  compounds  which  has  met  with  remarkable  success  in  accounting 
for  their  properties.  It  is  not  proposed  to  give  here  an  extended  exposi- 
tion of  Werner's  theory,  since  that  is  beyond  the  scope  of  this  mono- 
graph. However,  a  brief  outline  may  be  given  here,  in  order  to  make 
intelligible  the  relation  between  the  constitution  of  the  complex  metal- 
ammonia  salts  and  their  ionic  properties. 

According  to  Werner's  theory,  the  strongly  electronegative  elements 
or  groups  of  elements  are  attached  to  the  nuclear  atom  by  what  are  termed 
principal  valences,  while  neutral  groups  of  molecules  such  as  ammonia  are 
associated  with  the  nuclear  atom  by  auxiliary  or  secondary  valences.  A 
definite  number  of  atoms  or  groups  is  always  attached  to  the  nuclear  atom, 
either  by  principal  or  secondary  valences,  and  this  number,  which  is 
usually  6  and  sometimes  4,  is  fixed.  The  number  of  atoms  or  groups  so 
attached  is  called  the  co-ordination  number.  The  charge  on  the  nuclear 
complex  depends  upon  the  number  of  principal  valences  comprised  within 
the  co-ordination  number.  If  N  is  the  normal  valence  of  the  nuclear  atom, 
C  the  co-ordination  number  of  the  nuclear  group,  and  n  the  number  of 
secondary  valences  satisfied  in  the  nuclear  group  by  neutral  complexes, 
such  as  ammonia,  etc.,  then  the  number  of  charges  on  the  nuclear  group 
or  complex  is:  q  =  N  —  C  +  n.  Usually  the  co-ordination  number  is 
6  or  4.  If,  for  example,  the  co-ordination  number  is  6  and  the  normal 
valence  of  the  nuclear  atom  is  4,  then,  if  n  =  2,  that  is  if  two  molecules 
are  associated  in  the  nuclear  complex,  q  =  0,  and  the  charge  on  the  com- 
plex will  be  zero.  If,  on  the  other  hand,  n  were  0,  the  charge  on  the 
nuclear  complex  would  be  —  2 ;  that  is,  the  nuclear  complex  would  carry 
two  negative  charges.  On  the  other  hand,  if  n  were  6,  q  =  +  4;  that  is, 
the  nuclear  complex  would  carry  4  positive  charges.  For  a  co-ordination 
number  6,  the  maximum  variation  in  the  charge  on  the  nuclear  complex 
is  from  4  positive  to  2  negative  charges.  An  example  will  serve  to  make 
the  relationships  clear.  Platinum  chloride,  PtCl4,  in  which  platinum 
appears  with  the  principal  valence  of  4,  forms  with  ammonia  the  follow- 
ing series  of  complexes,  all  of  which  are  known  except  the  second. 

"  Werner,  New  Ideas  on  Inorganic  Chemistry.     Trans,  by  E.  P.  Hedley,  1011. 


CARRIERS  IN  ELECTROLYTIC  SOLUTIONS  211 

1  23  4  567 

Chloride  of  Platini-      Platinimpno-      Platini-       Cossa's    Potassium 

Drechsel's       Unknown      diammine       diammine       diammine     second      platinum 
base  chloride          chloride          chloride         salt         chloride 

Those  elements  or  groups  appearing  with  platinum  within  the  brackets 
are  contained  in  the  nucleus,  while  those  without  the  brackets 
carry  charges  and  are  capable  of  ionization.  The  co-ordination  number 
of  platinum  in  the  nucleus  is  6.  The  charge  on  the  nucleus  is  therefore 
given  by  the  equation  q  =  4  — 6  +  n,  where  n  is  the  number  of  ammonia 
molecules  in  the  complex.  In  the  first  compound  [Pt(NH3)6]Cl0  n  =  6 
and  q  =  +  4.  This  compound  therefore  ionizes  according  to  the  equa- 
tion: [Pt(NH3)6]Cl4=  [Pt(NH3)6]++"  +  4CK  On  the  other  hand,  in 
the  compound  [PtCl6]K2,  n  =  Q  and  q  =  —  2.  This  compound,  there- 
fore, ionizes  according  to  the  equation:  [PtCl6]K2  =  PtCl6~  +  2K+. 
The  manner  in  which  the  ionization  takes  place  in  the  other  compounds 
may  obviously  be  derived  from  the  equation  given.  If  Werner's  theory 
is  correct,  then,  when  the  various  compounds  are  dissolved  in  water,  the 
conductance  of  the  resulting  solutions  should  vary  in  correspondence  with 
the  number  of  changes  involved  in  the  ionization  reaction.  At  low  con- 
centrations, the  conductance  of  the  first  compound  should  lie  in  the 
neighborhood  of  500;  that  of  the  third  compound,  in  the  neighborhood  of 
200;  that  of  the  fourth,  in  the  neighborhood  of  100;  while  that  of  the 
fifth  should  be  zero.  On  the  other  hand,  that  of  the  sixth  should  lie  in 
the  neighborhood  of  100  and  that  of  the  seventh  in  the  neighborhood  of 
200.  In  solutions  of  these  last  two  compounds,  the  platinum  complex 
should  appear  as  anion.  This  consequence  of  Werner's  theory  has  been 
confirmed  by  experiment.  The  conductance  of  the  first,  third,  fourth, 
fifth,  sixth  and  seventh  compounds  at  0°  and  at  a  dilution  of  1000  liters 
are  respectively:  522.9,  228,  96.75,  0,  108.5,  and  256. 

The  conductance  of  the  fifth  compound  is  actually  not  quite  zero, 
since  in  solution  compounds  of  this  type  are  not  entirely  stable  and  reac- 
tion takes  place  with  the  water,  wherein  molecules  of  water  enter  the 
nucleus  and  thus  produce  a  charged  complex,  the  water  functioning  in  a 
manner  similar  to  that  of  ammonia.  However,  in  many  cases  values  of 
A  less  than  unity  have  been  obtained,  and  it  has  been  shown  that  the 
conductance  is  a  function  of  the  time  and  that,  moreover,  the  reaction  is 
catalyzed  at  the  electrode  surfaces.16* 

There  can  be  no  doubt  but  that  the  ionization  of  the  complex  metal- 
ammonia  and  other  similar  salts  depends  upon  the  combination  of  am- 

"»  Werner  and  Herty,  Ztachr.  f.  phya.  Chem.  38f  331   (1901). 


212        PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

monia  with  the  nuclear  atom.  What  characterizes  these  compounds  in 
particular  is  their  stability.  Similar  relations  may  exist  in  the  case  of 
other  salts  which  show  a  pronounced  tendency  to  form  complexes,  such  as 
calcium  salts  for  example,  but  in  these  cases  reaction  between  the  com- 
plex and  the  solvent  medium  takes  place  very  rapidly.  The  behavior  of 
these  complexes  in  water  does  not  differ  greatly  from  that  of  calcium 
chloride  in  propyl  alcohol,  whose  ionization  is  greatly  increased  on  the 
addition  of  water.  On  the  other  hand,  it  is  to  be  borne  in  mind  that  in 
non-aqueous  solutions  those  salts  which  exhibit  only  a  slight  tendency  to 
form  complexes  with  water  are  highly  ionized  in  all  cases.  This  is 
particularly  true,  for  example,  of  potassium  salts.  It  appears  probable 
that  such  salts  do  not  form  complexes  similar  to  the  metal-ammonia 
salts.  It  is  probable,  however,  as  we  have  seen,  that  all  ions  are  hydrated. 
It  appears  likely  that  the  solvent  molecules  may  be  associated  with  the 
ions  in  several  ways.  Certain  of  the  solvent  molecules  may  be  combined 
in  a  more  or  less  definite  manner,  as  in  the  metal-ammonia  complexes, 
while  other  molecules  may  be  associated  with  the  ions  due  to  the  opera- 
tion of  purely  electrical  forces. 

7.  Positive  Ions  of  Organic  Bases.  With  the  exception  of  ions  of 
salts  of  organic  bases  and  a  few  salts  of  the  type  of  the  ammonium  salts, 
the  positive  ions  consist  essentially  of  metallic  elements.  This  tendency 
of  the  metallic  elements  to  form  electropositive  ions  is  in  harmony  with 
prevailing  conceptions  regarding  atomic  structure.  The  organic  bases 
are  derived  from  the  less  electropositive  elements  on  the  introduction  of 
organic  radicals,  such  as  alkyl  and  aryl  radicals,  into  combination  with 
the  nuclear  element.  The  number  of  carbon  radicals  introduced  depends 
upon  the  valence  of  the  element  in  question,  and  upon  its  position  in  the 
periodic  system.  For  elements  up  to  the  fifth  group,  the  organic  bases 
have  the  constitution:  Rn_-jMnX,  where  n  is  the  maximum  valence  of  the 
element  with  respect  to  negative  elements.  For  elements  of  the  fifth  to 
the  seventh  groups,  inclusive,  the  bases  have  the  constitution:  R^,  ^MnX, 

where  n  is  the  valence  of  the  element  toward  hydrogen.  Thus,  we  have 
the  organic  bases:  CH3HgOH,  (CH3)2T10H,  (CH3)3SnOH,  (CH3)4NOH, 
(CH3)3SOH  and  (C6H5)2IOH.  The  strength  of  the  organic  bases  de- 
pends upon  their  constitution.  As  hydrogen  is  substituted  by  organic 
groups,  particularly  alkyl  groups,  the  strength  of  the  base  in  general 
increases,  although  a  marked  increase  does  not  take  place  until  the  sub- 
stitution of  the  last  hydrogen  atom  occurs,  in  which  case  the  resulting 
base  exhibits  a  maximum  strength.  Thus,  monomethyl-,  dimethyl-  and 
trimethylammonium  hydroxides  are  comparatively  weak  bases,  while 


CARRIERS  IN  ELECTROLYTIC  SOLUTIONS  213 

tetramethylammonium  hydroxide  is  a  base  whose  strength  is  practically 
the  same  as  that  of  potassium  hydroxide.  The  positive  ions  of  the  strong 
organic  bases  possess  distinct  metallic  characteristics  in  their  compounds. 
With  a  few  exceptions,  these  ionic  groups  may  not  be  obtained  in  a  free 
neutral  state,  since  in  this  condition  they  are  comparatively  unstable, 
yielding,  as  a  rule,  various  neutral  organic  compounds.  The  tetramethyl- 
ammonium group,  as  indeed  the  ammonium  group  itself,  possesses  an 
appreciable  stability.  So,  for  example,  the  ammonium  group  forms  an 
amalgam  in  which  the  presence  of  the  free  ammonium  group  has  been 
established.17  The  tetramethylammonium  group  forms  a  stable,  solid, 
metallic  amalgam  with  mercury,18  and  this  group,  moreover,  may  be  pre- 
cipitated in  a  free  state  by  electrolysis  in  ammonia  solution.19  Under 
these  conditions  the  free  group  dissolves  in  ammonia  to  form  a  solution 
which  resembles  solutions  of  the  alkali  metals  in  the  same  solvent.  These 
solutions,  however,  are  relatively  unstable  so  that  their  properties  have 
not  been  further  investigated. 

The  mercury  group,  CH3Hg,  has  been  obtained  in  a  free  state  by  elec- 
trolytic precipitation  from  an  ammonia  solution.20  The  free  group  is  a 
distinctly  metallic  substance  which  is  a  good  conductor  of  the  electric 
current.  This  group,  while  relatively  stable  in  comparison  with  other 
groups,  nevertheless  reacts  slowly,  even  at  low  temperatures,  and  at  high 
temperatures  it  reacts  instantaneously  according  to  the  equation: 


g  =  Hg  +  Hg(CH3)2. 

Not  only  do  the  ions  of  the  organic  bases,  therefore,  resemble  the  metallic 
elements,  but  the  free  basic  groups  themselves,  when  they  possess  suffi- 
cient stability  to  admit  of  their  being  isolated,  exhibit  metallic  properties. 
The  metallic  state  of  a  substance  is  not  one  characteristic  merely  of  ele- 
ments which  themselves  are  metallic  in  the  elementary  condition,  but 
includes  likewise  various  groups  of  elements  whose  constitution  is  such 
that  they  carry  a  negative  electron  which  is  relatively  loosely  attached  to 
the  group. 

8.  Complex  Anions.  Our  knowledge  of  the  structure  of  anion  com- 
plexes is  comparatively  limited.  No  data  are  so  far  available  which 
definitely  establish  that  the  anions  in  water  are  hydrated.  It  is  true, 
that,  from  the  conductance  values  of  the  anions  and  the  hydration  values 
of  the  cations,  it  may  be  inferred  that  the  anions  are  likewise  hydrated, 
but  the  hydration  of  the  anions  has  not  been  experimentally  verified. 

"Coehn,  Ztschr.  f.  Anorg.  Chem.  25,  430   (1900). 
18  McCoy  and  Moore,  J.  Am.  Chem.  Soc.  S3,  273   (1911). 

"Palmaer,  Ztschr.  g.  Electroch.  8,  729  (1902)  ;  Kraus,  V.  Am.  Chem.  Soc.  S5,  1732 
(1913)  . 

»  Kraus,  Joe.  cit. 


214        PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

The  existence  of  definite  anion-complexes  comparable,  for  example, 
with  those  of  the  cobalt  and  chromium  salts  is  not  indicated  by  the  proper- 
ties of  electrolytes,  either  in  solution  or  in  the  solid  and  liquid  state.  The 
anions  often  consist  of  definite  groups  containing  one  or  more  electro- 
negative atoms.  Among  these  we  have,  for  example,  the  nitrates,  chlo- 
rates, sulphates  and  other  common  anions,  as  well  as  many  anions  of 
organic  acids.  So  far  as  the  degree  of  ionization  is  concerned,  salts  of 
compound  anions  exhibit  properties  similar  to  those  of  salts  of  simple 
anions.  The  ionization  of  the  hydrogen  derivatives,  namely  the  acids, 
of  such  anions,  however,  is  largely  dependent  upon  the  nature  of  the 
atoms  occurring  in  the  anion  complex.  The  introduction  of  strongly 
electronegative  elements  into  the  anion  complex  increases  the  strength, 
that  is,  the  ionization  of  the  acid.  This  behavior  of  the  acids  is  so  well 
known  that  details  need  not  be  introduced  here. 

Certain  elementary  ions  form  complex  anions  with  the  same  or  other 
elements,  a  more  or  less  complex  equilibrium  existing  among  the  various 
complex  anions  formed  in  solution.  The  most  common  example  of  a 
complex  anion  of  this  type  is  the  complex  iodide  ion  which  is  formed 
by  the  direct  interaction  of  the  iodide  ion  with  iodine,  forming  the  ion 
I-.I2.  The  equilibrium  in  the  case  of  the  tri-iodide  ion  has  been  exten- 
sively studied  by  a  number  of  investigators.  The  mean  composition  of 
the  solution  in  such  cases  depends  upon  the  concentration,  since  the 
equilibrium  between  the  simple  and  the  complex  ion  is  a  function  of  the 
concentration.21 

It  is  well  known  that  the  halogen  salts  form  various  complexes  with 
other  halogens,  thus  indicating  that  complex  anions  are  formed  between 
a  halogen  ion  of  one  element  with  other  elements  of  the  halogen  group. 
The  chlor-iodides  are  familiar  examples  of  this  type.  The  equilibrium 
in  the  case  of  these  complex  anions  has  not  been  extensively  studied. 

The  work  of  Klister  22  indicates  that  the  normal  sulphide  ion  reacts 
with  excess  sulphur  to  form  a  series  of  complex  sulphur  anions.  These 
anions  appear  to  be  comparable  with  the  complex  iodide  ion,  the  charge 
being  associated  with  the  original  sulphide  anion.  The  mean  composition 
of  a  solution  of  sodium  sulphide  in  equilibrium  with  free  sulphur  varies 
as  a  function  of  the  concentration.  The  problem  in  the  case  of  aqueous 
solutions  is  complicated  owing  to  hydrolysis.  The  behavior  of  aqueous 
solutions  of  the  alkali  selenides  and  tellurides  indicates  that  these  metals 
also  form  complex  anions  in  the  presence  of  excess  of  these  metals.23 
They  have  not,  however,  been  extensively  investigated. 

«»Bray  and  MacKay,  J.  Am.  Chem.  Soc.  32,  915   (1910). 

"Ktister  and  Heberlein,  Ztachr.  f.  Anorg.  Chem.  43,  53  (1905)  ;  Kiister,  ibid.,  A4.  431 
(1905).  «Tibbals,  J.  Am.  Chem.  Soc.  31,  902  (1909). 


CARRIERS  IN  ELECTROLYTIC  SOLUTIONS  215 

Solutions  of  complex  selenides  and  tellurides  have  been  obtained  in 
liquid  ammonia  by  the  action  of  the  normal  salts  on  the  free  elements.24 
Solutions  of  the  complex  tellurides  in  liquid  ammonia  are  the  only  ones 
which  so  far  have  been  extensively  investigated.  The  normal  telluride, 
which  is  only  slightly  soluble  in  ammonia,  is  formed  by  the  direct  action 
of  the  metal  on  sodium  in  ammonia  solution.  The  telluride  so  formed 
is  a  white  substance,  apparently  somewhat  crystalline  in  character.  In 
the  presence  of  excess  tellurium  the  normal  telluride  reacts  with  the  metal, 
forming  a  complex  tellurium  salt  which  is  very  soluble  in  ammonia.  The 
composition  of  the  solution  in  equilibrium  with  a  normal  telluride  Na2Te 
is  Na2Te2.25  Apparently  the  following  reaction  takes  place: 

Na*Te  solid  +  Te  solid  =  Na2Te*  solution- 

This  solution  exhibits  an  intense  violet  blue  color.  When  the  normal 
telluride  Na2Te  has  disappeared,  the  complex  Na2Te2  in  solution  reacts 
with  free  tellurium  to  form  another  complex.  In  concentrated  solutions 
the  composition  of  the  ammonia  solution  corresponds  very  nearly  with 
Na2Te4.  The  exact  value  of  the  composition,  however,  is  a  function  of 
the  concentration,  the  amount  of  tellurium  in  solution  decreasing  at  lower 
concentrations.26  The  color  of  the  solution  in  equilibrium  with  metallic 
tellurium  is  deep  red. 

The  molecular  weight  of  the  telluride  in  equilibrium  with  metallic 
tellurium  has  been  determined  and  found  to  correspond  with  the  formula 
Xu2Te.Tex;  that  is,  sodium  is  associated  with  a  divalent  complex  tel- 
lurium anion.27 

While  the  normal  telluride  is  a  white  substance  exhibiting  only  non- 
metallic  characteristics,  the  product  resulting  on  evaporating  a  solution 
containing  larger  amounts  of  tellurium  is  metallic  in  appearance,  indicat- 
ing that  the  salts  of  the  complex  tellurides  are  metallic  substances.  This 
behavior  of  the  complex  tellurides  in  the  free  state  is  particularly  im- 
portant when  we  come  to  consider  similar  complex  anions  of  metals  of 
the  fourth  and  fifth  groups. 

Whereas  our  knowledge  of  the  complex  anions  of  this  type  has  pre- 
viously been  restricted  chiefly  to  elements  of  the  sixth  and  seventh 
groups,  in  recent  years,  through  a  study  of  solutions  in  liquid  ammonia, 
evidence  has  come  to  light  which  indicates  that  the  elements  of  the 
fourth  and  fifth  groups  form  complex  anions  similar  in  character  to  the 
complex  sulphide  and  iodide  ions.  In  the  case  of  the  salts  of  these  com- 

"Hugot,  Compt.  rend.,  129,  299  and  388   (1899). 

85Chiu,  Dissertation,  Clark  University  (1920). 

*»  E.g.  Chiu,  loc.  cit. 

87  E.  H.  Zeitfuchs,  Dissertation,  Clark  University   (1921). 


216        PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

plex  anions,  however,  the  non-metallic  characteristics  have  disappeared, 
and  these  substances  in  the  solid  state  are  metals.  In  solution,  how- 
ever, they  exhibit  properties  similar  to  those  of  tellurium.  A  charac- 
teristic property  of  such  solutions  is  the  existence  of  anions  of  distinctly 
metallic  elements.  Thus,  lead  is  precipitated  on  the  anode  when  the 
current  is  passed  through  a  solution  containing  the  complex  Na4Pb.Pbx.28 
A  similar  result  has  been  obtained  in  the  case  of  the  antimony  complex 
Na3Sb .  Sbx.29  In  a  solution  of  the  lead  complex  in  equilibrium  with  lead, 
2.25  atoms  of  lead  are  precipitated  on  the  anode  per  equivalent  of  elec- 
tricity.30 This  corresponds  with  the  mean  composition  of  the  solution. 
The  proportion  of  lead  to  sodium  in  the  presence  of  excess  lead  is  inde- 
pendent of  the  concentration  of  the  solution.  In  the  case  of  the  anti- 
mony complex,  the  mean  composition  of  the  solution  is  a  function  of 
the  concentration.  The  maximum  lies  in  the  neighborhood  of  0.4  N 
sodium.31  At  lower  concentrations,  the  mean  composition  falls  off 
sharply  from  the  value  2.33  at  the  maximum  to  1.2  at  a  concentration  of 
0.005  N.  Bismuth  and  tin  likewise  form  complexes  of  a  similar  nature 
which  have  not  thus  far  been  studied  in  detail. 

The  solutions  of  these  complexes,  except  possibly  at  the  highest  con- 
centrations, are  purely  electrolytic  in  character.32  While  the  number  of 
charges  associated  with  the  negative  complex  has  not  been  definitely 
determined  in  the  case  of  lead  and  antimony,  it  is  probable  that  the 
charges  are  respectively  4  and  3,  corresponding  with  the  position  of  these 
elements  in  the  periodic  system.  It  is  evident  that  many  metallic  ele- 
ments are  capable  of  forming  complex  anions  similar  to  the  complex 
sulphur  and  iodide  ions.  The  compounds  which  are  left  behind  on 
evaporation  of  ammonia  are  metallic.  In  view  of  the  electrolytic  prop- 
erties of  these  compounds  when  in  solution,  it  appears  probable  that  the 
solid  compounds  themselves  are,  in  fact,  salt-like  in  character,  the  more 
electronegative  element  carrying  a  negative  charge.  The  existence  of  a 
large  number  of  compounds  in  binary  systems,  such  as  those  of  sodium 
and  lead,  is  probably  due  to  the  formation  of  negative  ionic  complexes. 
In  all  likelihood,  this  property  is  not  confined  to  the  metals  whose  com- 
pounds are  soluble  in  ammonia.  It  is  probable  that  the  constitution  of 
the  compounds  formed  between  the  strongly  electropositive  elements  and 
such  elements  as  thallium  and  mercury  is  similar  to  those  of  lead. 

9.  Other  Complex  Ions.  Complex  anions  are  formed  by  many  salts 
of  metallic  and  non-metallic  elements  on  interaction  with  salts  of  the 

MKraus,  J.  Am.  Chem.  Soc.  29,  1557  (1907)  ;  Smyth,  ibid..  39,  1299  (1919). 

"Peck,  J.  Am.  Chem.  Soc.  40,  335   (1918). 

»°  Smyth,  loc.  cit. 

81  Peck,  loc.  cit. 

"Kraus,  J.  Am.  Chem.  Soc.  #,  752  (1921). 


CARRIERS  IN  ELECTROLYTIC  SOLUTIONS  217 

more  electropositive  elements.  Many  such  complex  anions  have  been 
investigated  in  which  mercury,  tin,  lead,  platinum,  silicon  and  other  ele- 
ments appear  in  the  anion  complex  in  association  with  strongly  electro- 
negative elements  such  as  chlorine,  fluorine,  etc.  The  constitution  of 
these  complex  anions  is  accounted  for  by  Werner's  theory  which  has 
already  been  briefly  outlined. 

Complex  or,  preferably,  intermediate  ions,  both  positive  and  negative, 
may  be  formed  when  salts  of  higher  type  ionize  in  stages.  Such  ions 
have  many  representatives  among  the  higher  types  of  weak  acids  and 
bases  when  the  ionization  constants  of  the  different  ions  have  different 
values.  This  is  the  case,  for  example,  with  phosphoric  acid. 

Whether  similar  complex  ions  are  commonly  formed  in  solutions  of 
salts  of  higher  type  is  uncertain.  The  cation  transference  number  of 
cadmium  iodide  at  high  concentrations  is  greater  than  unity,  which 
clearly  indicates  the  existence  of  an  intermediate  cadmium  ion.  In  the 
case  of  other  salts,  the  existence  of  intermediate  ions  is  not  definitely 
established  although,  as  we  shall  see  below,  the  existence  of  such  ions  in 
mixtures  may  be  inferred  from  solubility  data.  There  are  no  data 
available  relative  to  the  existence  of  similar  ions  in  non-aqueous  solu- 
tions. It  is  possible,  also,  that  binary  electrolytes  may  associate  and 
dissociate  with  the  formation  of  complex  ions.  Their  existence  has  not 
been  established. 


Chapter  IX. 
Homogeneous  Ionic  Equilibria. 

1.  Equilibria  in  Mixtures  of  Electrolytes.  If  the  constituents  in  a 
mixture  of  two  or  more  electrolytes  obey  the  mass-action  law,  then  the 
equilibrium  in  the  mixture  may  at  once  be  determined  if  the  values  of 
the  mass-action  constants  are  known.  The  values  of  these  constants 
may  in  general  be  determined  from  a  study  of  solutions  of  the  pure 
substances  under  corresponding  conditions.  The  equations  underlying 
such  equilibria  have  the  form: 

C+C~ 


where  C+  denotes  the  concentration  of  the  positive  ions,  C~  that  of  the 
negative  ions,  and  Cu  that  of  the  un-ionized  fraction  of  a  given  elec- 

trolyte. K  is  the  ionization  constant  of  the  electrolyte  in  question.  For 
every  electrolyte  appearing  in  the  solution  as  an  un-ionized  molecule, 
the  concentrations  of  its  un-ionized  fraction  and  of  its  ions  appear  as 
variables.  In  general,  these  ions  will  also  be  common  to  other  electro- 
lytes present  in  the  mixture.  The  total  number  of  ionic  species  in  solu- 
tion will  be  equal  to  the  total  number  of  un-ionized  species  in  solution 
in  case  any  number  of  electrolytes  without  a  common  ion  are  mixed. 
The  mass-action  law  leads  to  a  series  of  reaction  equations  of  the  type: 

M,+  X  XT  =  l^MA, 

and  the  concentrations  of  the  various  molecular  species  present  in  the 
solution,  and  to  a  series  of  condition  equations  of  the  type: 


and    MXX±  +  MA  +  .  .  .  +  Xr  =  Cx^ 

The  number  of  equations  will  always  be  equal  to  the  number  of  variables 
and  the  concentrations  of  the  various  molecular  species  present  in  the 
solution  may  be  determined  by  solving  the  resulting  simultaneous  equa- 
tions. If  two  electrolytes  without  an  ion  in  common  are  mixed,  the 
resulting  reaction  equations  are: 

218 


HOMOGENEOUS  IONIC  EQUILIBRIA  219 

M^XX.-^^M.X, 

M2+  X  X2-  = 


and  the  condition  equations  are: 

Mx  +  MA  +  MXX2  =  C 
M2  +  M2X2  +  MA  =  C 


where  C±  and  C2  are  the  total  concentrations  of  the  base  M±  or  acid  X1? 
which  are  necessarily  equivalent,  and  the  base  M2  or  the  acid  X2>  which 
are  likewise  equivalent.  From  these  eight  equations  the  concentrations 
of  the  eight  different  molecular  species  may  be  determined  for  any  con- 
centrations Cj.  and  C2  of  the  total  acids  and  the  total  bases  in  solution. 
In  this  case,  interaction  with  the  solvent  is  assumed  not  to  take  place. 
In  a  mixture  of  two  electrolytes  with  a  common  ion  we  have  the  reaction 
equations  : 

M!+  X  X-  =  K^U.X 

M2+  X  X-  =  #2M2X 

and  the  condition  equations: 

M,X  +  Mx  =  Cx 
M,X  +  M2  =  C2 
MXX  +  M2X  +  X  =  Cx  +  C2. 

In  this  case  the  solution  of  the  problem  is  comparatively  simple. 

In  a  mixture  of  two  electrolytes  having  an  ion  in  common,  assuming 
the  mass-artion  law  to  hold,  the  ionization  of  the  electrolytes  in  the  mix- 
ture will  be  the  same  as  that  in  the  original  solutions  before  mixing,  if 
the  concentrations  of  the  qommon  ion  in  these  solutions,  before  mixing, 
are  equal.  Such  solutions  are  said  to  be  isohydric.1  This  result  is  a 
consequence  of  the  law  of  mass-action.  Let  M±+,  M2+  and  X~  be  the 
concentrations  of  two  solutions  having  in  common  the  ion  X~.  It  is 
obvious  that  the  concentration  of  the  common  ion  in  these  two  solutions 
will  be  equal  to  M/  for  the  first  solution  and  M2+  for  the  second  solution. 
Let  a  volume  Vt  liters  of  the  first  solution  be  mixed  with  a  volume  of  V2 
liters  of  the  second  solution.  If  the  concentrations  of  the  ion  X~  in  the 
two  original  solutions  are  equal,  then  we  obviously  have: 

Mx+  =  M2+  =  X-. 

1  Arrheniua,  Ann.  d.  Phj/s.  S0f  51  (1887)  ;  Ztachr.  /.  phys.  Chem.  2,284  (1888)  ;  t&id., 
5,  1  (1890). 


220        PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

In  the  mixture,  therefore,  assuming  that  no  displacement  of  the  equi- 
librium takes  place,  we  should  have  for  the  concentration  of  the  ions  Mx+ 

the  value        1+   *  ,  for  that  of  the  common  ion  — *     *  J"  v  2 — -  and  for 

V,  +  V2  Y!  -j-  V2 

y 
that  of  the  un-ionized  fraction  M^,,     *  y  .    If  the  law  of  mass-action 

1     I          2 

holds,  we  have  the  equation: 


If  M!+  =  M2+,  the  expression  for  the  concentration  of  the  common  ion 
becomes : 


and  the  equilibrium  equation  reduces  to: 

M±+  x  xx-  _ 


In  other  words,  if  the  concentration'  of  the  common  ion  is  the  same  in  the 
original  solutions,  then,  if  these  solutions  are  mixed  in  any  proportion, 
assuming  no  change  in  the  equilibrium  to  take  place,  the  concentrations 
of  the  ions  in  the  mixture  will  be  such  as  to  fulfill  the  conditions  necessary 
for  equilibrium. 

The  correctness  of  this  principle  may  readily  be  tested  in  the  case  of 
weak  acids.  Since  the  conductance  in  solutions  of  the  acids  is  due  chiefly 
to  the  conductance  of  the  hydrogen  ion,  it  follows  that  two  acids  will 
have  the  same  concentration  of  the  hydrogen  ion  when  the  solutions 
have  the  same  specific  conductance.  Therefore,  a  mixture  of  two  solu- 
tions fulfilling  these  conditions  will  have  the  same  specific  conductance 
as  the  original  solutions.  If  the  anions  have  different  conductance 
values,  the  specific  conductance  of  isohydric  solutions  will  differ  in 
proportion  to  the  conductance  of  these  anions,  and  the  specific  conduct- 
ance of  a  mixture  of  the  solutions  will  be  the  arithmetic  mean  of  that 
of  the  components.  This  principle  has  been  extensively  tested  by  the 
conductance  as  well  as  other  methods  and  has  been  shown  to  hold  true 
for  mixtures  of  weak  acids  and  bases. 

It  has  been  found,  however,  that  even  in  solutions  which  do  not  con- 
form to  the  law  of  mass-action,  that  is,  in  solutions  of  strong  electrolytes, 


HOMOGENEOUS  IONIC  EQUILIBRIA  221 

a  similar  condition  holds.  If,  for  example,  solutions  of  sodium  chloride 
and  potassium  chloride  have  the  same  ion  concentration,  then,  on  mixing, 
the  concentration  of  the  ions  in  the  mixture  will  be  the  same  as  that  in 
the  original  solutions.  Apparently,  then,  the  isphydric  principle  holds, 
even  in  the  case  of  electrolytes  which  do  not  obey  the  law  of  mass-action. 
This  principle  has  been  employed  very  extensively  for  the  purpose  of 
calculating  the  concentrations  in  mixtures  of  strong  electrolytes.  If  the 
electrolytes  in  a  given  mixture  do  not  obey  the  law  of  mass-action,  then 
it  is  obviously  impossible  to  calculate  the  equilibrium  in  the  mixture 
unless  we  know  the  law  governing  this  equilibrium.  The  isohydric  prin- 
ciple is  an  empirical  relation  which  has  been  assumed  to  govern  the 
equilibrium  in  mixtures.  In  order  to  test  the  correctness  of  this  prin- 
ciple, it  is  obviously  necessary  to  determine  the  concentrations  of  the 
ions  in  the  mixture  by  some  independent  means. 

The  law  of  equilibrium  for  a  given  electrolyte  in  a  mixture  must 
reduce  in  the  limit  to  that  of  a  solution  of  the  electrolyte  in  the  pure 
solvent.  It  has  been  shown  that,  for  a  strong  electrolyte,  Equation  11 
holds  very  nearly.  According  to  this  equation,  the  ratio  of  the  product 
of  the  concentrations  of  the  ions  divided  by  the  concentration  of  the 
un-ionized  fraction  varies  as  an  exponential  function  of  the  ion  concen- 
tration. It  is  clear  that  this  relation  conforms  to  the  principle  of  iso- 
hydric solutions.  In  a  mixture  of  electrolytes,  the  equation  might  take 
the  form: 

u 

where  P^  is  the  value  of  the  ion  product,  Cu  is  the  concentration  of  the 
un-ionized  fraction,  and  C^  is  the  total  concentration  of  the  positive  or 

negative  ions  in  the  mixture.  Indeed,  it  is  apparent  that  an  equation 
of  the  form: 

(51)  ??-=F(ZC) 

Lu 

will  conform  to  the  isohydric  principle,1  where  F(2C^)  is  any  explicit 
function  of  the  total  ion  concentration  of  the  mixture.  For,  on  mixing 
two  solutions  whose  ion  concentrations  are  C*  and  C^",  the  equilibrium 
will  be  unaffected  by  the  relative  volumes  of  the  solutions  mixed,  pro- 

>Arrhenius,  Ztschr.  f.  phys.  Chem.  31,  218  (1899). 


222        PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 
vided  that  C/  and  C/'  are  equal.    Equation  51,  therefore,  is  the  analyti- 

V  V 

cal  expression  of  the  isohydric  principle.  In  the  limit,  as  the  second  com- 
ponent in  the  mixture  disappears,  the  equation  reduces  to  that  for  the 
first  salt  alone.  In  the  case  of  mixtures  of  electrolytes  without  a  com- 
mon ion  the  same  expression  applies. 

Equation  51  is  not  the  only  function  which  might  be  assumed  to  hold 
for  the  mixture  which  reduces  to  the  form  of  Equation  11  in  the  case 
of  a  solution  of  a  single  electrolyte.  We  might  assume  for  the  mixtures 
a  function  of  the  form: 

Pt 
(52)  -^-=F(P.)9 

^u 

where  again  P^  is  the  ion  product.    In  the  limit  the  concentrations  of 

the  positive  and  negative  ions  become  equal  for  the  solution  of  a  single 
salt,  and  consequently  this  equation  reduces  to  the  form  of  Equation  11. 
The  isohydric  principle,  or  more  generally,  the  iso-ionic  principle,  is  a 
consequence  of  the  law  of  mass-action,  but,  when  the  law  of  mass-action 
fails  to  hold,  there  is  no  reason  for  assuming  that  Equation  51  rather 
than  Equation  52  is  correct,  for  both  reduce  to  the  same  limiting  form 
in  the  case  of  a  solution  of  a  single  electrolyte.  We  may,  therefore, 
inquire  which  of  the  two  functions  corresponds  most  nearly  with  the 
experimental  values. 

In  order  to  test  the  functions  in  the  case  of  mixtures,  it  is  obviously 
necessary  to  measure  some  property  of  these  mixtures  by  independent 
means,  as,  for  example,  the  conductance  of  a  mixture  of  electrolytes. 
Assuming  that  the  conductance  of  the  ions  in  the  mixture  is  the  same  as 
that  of  the  same  ions  in  pure  solutions,  it  is  possible  to  calculate  the 
specific  conductance  of  the  mixture,  if  the  form  of  the  conductance  func- 
tion for  the  pure  electrolytes  is  known,  and  if  a  function  is  assumed  for 
the  mixture.  If  the  assumed  function  is  correct,  then  the  calculated 
specific  conductance  for  the  mixture  should  correspond  to  the  measured 
specific  conductance  of  the  mixture  within  the  limits  of  experimental 
error.  If  the  calculated  and  observed  values  do  not  correspond,  it  fol- 
lows that  the  function  assumed  for  the  mixture  is  not  correct.  That  an 
equilibrium  actually  exists  in  the  mixture  appears  to  be  beyond  question, 
although  the  exact  nature  of  the  reaction  may  be  somewhat  in  doubt. 

Bray  and  Hunt 2  have  measured  the  specific  conductance  of  mixtures 
of  sodium  chloride  and  hydrochloric  acid  in  water  at  25°.  They  have 
likewise  calculated  the  specific  conductance  of  the  mixtures,  assuming 

aBray  and  Hunt,  J.  Am.  Chem.  Soc.  S3,  781  (1911). 


HOMOGENEOUS  IONIC  EQUILIBRIA 


223 


the  isohydric  principle;  that  is,  assuming  Equation  51.  The  results  are 
given  in  Table  LXXXIII,  in  which  the  concentrations  of  sodium  chloride 
and  hydrochloric  acid  are  given  in  the  second  and  third  columns  re- 
spectively, and  the  measured  specific  conductance  is  given  in  the  fourth 
column.  In  the  fifth  column  is  given  the  specific  conductance  calculated 
on  the  assumption  of  the  iso-ionic  principle,  namely  Equation  51,  while  in 
the  seventh  column  is  given  the  value  of  the  calculated  specific  conduct- 
ance, assuming  Equation  52.  In  the  sixth  and  eighth  columns  are  given 
the  percentage  deviations  between  the  measured  and  calculated  values. 

TABLE  LXXXIII. 

MEASURED  SPECIFIC  CONDUCTANCE  OF  MIXTURES  OF  NaCl  AND  HC1  COM- 
PARED WITH  VALUES  CALCULATED  ACCORDING  TO  EQUATIONS  51  AND  52. 


Concentration 
(Approx.) 
millimols 
No.  NaCl     HC1 


Specific  Conductance  n 
Calculated 

Equa-  Calculated 

Measured   tion  51       %  Dif.    Equation  52 


%  Dif. 


1 

2 
3 
4 
5 
6 

100 
100 
100 
100 
100 
100 

100 
50 
20 
10 
5 
2 

47.25 
29.14 
18.06 
14.36 
12.52 
11.41 

48.21 
29.62 
18.31 
14.50 
12.59 
11.45 

2.1 
1.6 
1.4 
1.0 
0.6 
0.3 


Mean  —  1.15% 

7 

20 

50 

21.75 

21.89 

—  0.7 

8 

20 

20 

10.157 

10.27 

—  1.1 

9 

20 

10 

6.253 

6.307 

—  0.9 

10 

20 

4 

3.889 

3.919 

—  0.8 

11 

20 

2 

3.101 

3.118 

—  0.6 

12 

20 

1 

2.709 

2.721 

—  0.4 

Mean  — 


13 
14 
15 
16 


5 
5 
5 
5 

12.5 
5 
2 
1 

5.651 
2.632 
1.621 
1.011 

5.678 
2.650 
1.630 
1.016 

Mean  —0.57% 


47.09 
28.82 
17.84 
14.18 
12.39 
11.35 


Mean  +  0.85% 

21.65         +  0.4 
10.13         +  0;3 

6.221 

3.870 

3.094 

2.702 

Mean  +0.33% 

5.646  +  0.1 

2.634  —0.1 

1.619  +  0.1 

1.010  +  0.1 

Mean  +  0.05% 


Comparing  the  measured  values  of  the  specific  conductance  with  those 
calculated  on  the  basis  of  Equation  51,  it  is  seen  that  the  deviations  from 
the  iso-ionic  principle  are  consistently  larger  than  any  conceivable  experi- 
mental error.  In  the  case  of  0.1  normal  solutions  of  sodium  chloride,  the 


224        PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

mean  error  is  1.15  per  cent;  for  0.02  normal  solutions,  0.75  per  cent; 
and  for  0.005  normal  sodium  chloride  solutions,  the  mean  deviation  is 
0.57  per  cent.  At  the  lower  concentrations  the  agreement  is  measurably 
better  than  at  the  higher  concentrations,  a  result  which  is  perhaps  not 
unexpected,  since  at  concentrations  as  high  as  0.1  normal  viscosity  effects 
unquestionably  come  into  play.  The  agreement  between  the  measured 
and  calculated  values  based  on  Equation  52  is  markedly  better  than  that 
of  values  based  on  Equation  51.  In  the  case  of  the  0.1  normal  solutions  of 
sodium  chloride,  the  mean  deviation  is  0.85  per  cent.  In  the  mixtures 
of  sodium  chloride  of  concentration  0.02  and  0.005,  the  mean  deviations 
are  respectively  0.33  and  0.05  per  cent,  values  which  fall  very  nearly 
within  the  limits  of  experimental  error.  In  calculating  the  specific  con- 
ductances of  the  mixtures  according  to  Equation  52,  424  was  assumed 
for  the  value  of  A0  for  hydrochloric  acid  and  127  for  that  of  sodium 
chloride.  These  values  may  be  somewhat  in  error,  but  it  is  to  be  noted 
that  the  calculated  specific  conductances  are  affected  to  only  a  very 
small  extent  by  the  value  assumed  for  A0.  It  must  be  concluded  from 
these  results  that  the  isohydric  principle  is  not  applicable  to  mixtures 
of  strong  electrolytes.  In  the  case  of  the  mixtures  of  hydrochloric  acid 
and  sodium  chloride,  at  any  rate,  Equation  52  yields  results  which  corre- 
spond quite  closely  with  the  observed  values  at  low  concentrations.  It 
is  uncertain,  however,  that  a  similar  correspondence  will  be  found  in  the 
case  of  mixtures  of  other  electrolytes.  For  the  present,  therefore,  the 
form  of  the  function  which  should  be  assumed  in  the  case  of  mixtures  of 
strong  electrolytes  remains  doubtful. 

2.  Hydrolytic  Equilibria.  Water  itself  is  ionized  to  a  slight  extent 
into  hydrogen  and  hydroxyl  ions.  There  therefore  exists  in  water  an 
equilibrium  which,  if  the  law  of  mass-action  holds,  is  expressed  by  the 
equation: 


where  KW  is  the  ionization  constant  of  water.    The  concentration  of  the 

hydrogen  and  hydroxyl  ions  in  pure  water  has  been  determined  by 
Kohlrausch  from  the  conductance  of  very  pure  water.  At  18°  this  method 
yielded  the  value  0.80  X  10~7  for  the  concentration  of  the  hydrogen  and 
hydroxyl  ions  in  pure  water.  The  ionization  constant  has  also  been 
determined  from  the  electromotive  force  of  gas  cells,  from  the  rate  of 
certain  esterrification  reactions  and  from  the  hydrolysis  of  certain  salts 
in  water.  In  these  latter  methods,  an  electrolyte  has,  in  general,  been 
present,  which  naturally  introduces  an  uncertainty  as  to  the  effect  of 


HOMOGENEOUS  IONIC  EQUILIBRIA  225 

the  electrolyte  on  the  ionization  constant  of  water.    The  results  of  the 
various  methods  are  summarized  in  the  following  table. 

TABLE  LXXXIV. 

THE  HYDROGEN-ION  CONCENTRATION  (X  107)  IN  PURE  WATER  AS  DETER- 
MINED BY  VARIOUS  INVESTIGATORS. 

Investigator  Method  of  Determination  0°         18°       25° 

Arrhenius  ......  Hydrolysis  of  sodium  acetate  by 

ester-saponification   .................         1.1 

Wijs  ...........  Catalysis  of  ester  by  pure  water  ........         1.2 

Nernst   .........  Electromotive  force  of  gas  cell  ......         0.8 

Lowenherz    .....  Electromotive  force  of  gas  cell  .........       1.19 

Kohlrausch  and 
Heydweiller  .  .  Conductance  of  pure  water  .......     0.36      0.80      1.06 

Kanolt    ........  Hydrolysis   ....................     0.30      0.68      0.91 

When  a  salt  is  dissolved  in  water,  interaction  takes  place  between 
the  ions  of  the  salt  and  the  ions  of  water  with  the  resultant  formation 
of  un-ionized  molecules  of  acid,  or  of  base  or  of  both,  depending  upon 
the  strength  of  the  acid  and  the  base.  Assuming  the  law  of  mass-action 
to  hold  in  the  mixture  for  both  acid  and  base,  and  assuming  that  the 
salt  is  highly  ionized  and  that  its  ionization  function  is  known  and  is 
the  same  in  the  mixture  as  it  is  in  a  solution  of  the  salt  alone,  the  con- 
centration of  the  various  constituents  in  the  mixture  may  be  obtained 
from  a  solution  of  the  reaction  equations: 

H+  X  X-  =  # 
(53)  M+  X  OH-  = 


and  the  condition  equations: 

MX  +  HX  +  X-  =  Ca, 

(54)  MX  +  MOH  +  M+  =  C6, 

M+  +  H+  =  X-  +  OH-, 

where  Ka,  K^  and  KW  are  the  ionization  constants  of  acid,  base,  and 
water,  respectively,  and  Ca  and  C^  are  the  total  concentrations  of  acid 

and  of  base,  and  the  other  symbols  represent  the  concentrations  of  the 
various  constituents  concerned  in  the  reaction.  Let  us  assume  that  the 
acid  is  stronger  than  the  base,  in  which  case  H+  is  greater  than  OH~. 
Let  Y  represent  the  fraction  of  base  present  in  the  form  of  ions.  Since 


226        PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

M*  differs  from  X~,  ys  is  not  identical  with  the  ionization  of  the  salt, 
but,  unless  the  hydrolysis  is  great,  the  value  of  ys  will  not  differ  appre- 

ciably from  that  of  the  salt  at  the  concentration  in  question.  Let  h 
represent  the  total  fraction  of  base  present  in  the  un-ionized  condition, 
in  which  case  h  is  the  hydrolysis  coefficient.  A  solution  of  the  above 
equations  leads  to  the  equation: 


(55) 


The  concentrations  of  the  various  constituents  are  given  by  the  follow 
ing  equations: 


C- 


Kbh 


(l-h)          Kh 


K 
(56)  OH-  = 


Kbh 


_  _ 


MOH  =  hCb 

If  YS,  together  with  the  reaction  constants,  are  known,  the  concen- 

trations of  the  constituents  may  be  calculated.  The  equations  may  be 
generalized  by  introducing  the  ionization  function  KS  for  the  salt  by 
means  of  the  equation: 

(57)  M+  X  X-  =  £SMX. 

This  leads  to  the  equation: 


(58) 


HOMOGENEOUS  IONIC  EQUILIBRIA  227 

These  equations  are  independent  of  the  concentration  of  the  various 
reacting  constituents  so  long  as  the  assumed  conditions  are  fulfilled.  In 
many  instances  they  may  be  greatly  simplified  for  practical  purposes. 
If  the  concentration  of  the  salt  is  not  extremely  low  and  if  the  acid  is 
stronger  than  the  base,  the  concentration  of  the  hydroxyl  ions  may  be 


neglected  in  comparison  with  that  of  the  M+  ions,  and  the  term    -  —  -r 


Kbh 


may  be  dropped  out  of  the  equations.  If  the  hydrolysis  is  small,  the 
concentration  of  the  hydrogen  ions  may  be  neglected  in  comparison  with 
that  of  the  M+  ions.  The  equation,  then,  reduces  to  the  form: 


Kw 


v   v  r*         ft       i,\2  i    v    n    /t       it\° 

KaKb  Lb       (l~h)       Kbtb(l—h) 

If  acid  and  base  are  present  in  equivalent  amounts,  the  hydrolysis  of  the 
salt  is  expressed  by  the  equation: 


(!-*)«     KaKb  '  KbCb(l-h) 
and  the  hydrogen  ion  concentration  by: 

(61) 


KwKa      Kwy8Cbd-K) 

These  equations  are  generally  applicable,  provided  the  concentration  of 
the  hydrogen  ions  is  relatively  small  in  comparison  with  that  of  the  ions 
of  the  salt.  In  the  case  of  a  solution  of  a  strong  acid  and  a  weak  base, 
the  second  term  in  Equation  60  is  evidently  determinative  of  the  degree 
of  hydrolysis  of  the  salt,  while  in  solutions  in  which  both  the  acid  and 
base  are  very  weak  and  the  total  concentration  of  the  base  is  high,  the 
first  term  is  chiefly  determinative  of  the  hydrolysis.  In  the  case  of  acids 
and  bases  of  intermediate  strength,  and  particularly  at  fairly  low  con- 
centrations, both  terms  must  be  taken  into  account  in  determining  the 
hydrolysis  of  a  salt. 

In  very  dilute  solutions  of  salts  of  relatively  strong  acids  and  bases, 
it  is  possible  that  conductance  measurements  may  be  appreciably  affected 
by  hydrolysis.  This  is  particularly  true  if  the  limiting  values  of  the 
ionization  constant  approached  by  acid  and  base  differ.  It  is  obvious 
that  the  actual  concentration  of  acid  and  of  base  in  solution  is  very  low, 


228        PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

and  the  values  of  the  ionization  functions  to  be  introduced  for  acid  and 
base  are  therefore  not  the  values  for  these  ionization  functions  at  ordi- 
nary concentrations  of  acid  and  base,  but  rather  the  values  approached 
at  very  low  concentrations.  Actually,  we  do  not  know  the  limiting  value 
which  the  ionization  functions  approach  in  aqueous  solutions  of  strong 
acids  and  bases.  Consequently,  conductance  measurements  with  dilute 
salt  solutions  remain  in  doubt  so  long  as  the  values  of  the  ionization 
functions  remain  unknown.  It  is  fairly  certain  that  in  the  case  of  salts 
of  weaker  bases,  such  as  the  silver  salts,  for  example,  the  conductance 
must  be  measurably  affected  at  concentrations  below  10~3  normal.  Ac- 
cording to  Bottger,3  the  ionization  constant  of  silver  oxide  at  25°  is 
2.5  X  10~4.  Assuming  for  the  ionization  constant  of  water  the  value 
0.91  X  10~14  and  assuming  that  the  ionization  of  the  salt  is  practically 
complete,  we  obtain  the  following  values  for  the  hydrolysis  of  silver 
salts  at  25°. 

TABLE   LXXXV. 
HYDROLYSIS  OF  SILVER  SALTS  AT  DIFFERENT  CONCENTRATIONS  AT  25°. 

C    10-3  10-*  10-5 

h  1.9  X10-4        6.0  X10-4        1.9  X10-4 

Cond.  inc 5.7  X  10'4        1.8  X  10'3        5.7  X  10'3 

As  a  result  of  the  replacement  of  Ag+  ions  by  H+  ions  in  the  solution, 
the  conductance  is  increased  approximately  in  the  ratio  of  one  to  three. 
In  the  third  line  of  the  above  table  are  given  values  of  the  increase  in 
the  conductance  due  to  the  hydrolysis  of  the  salt.  It  is  seen  that  even 
at  10"3  normal  the  conductance  of  a  silver  salt  is  affected  to  the  extent 
of  0.057%,  while  in  a  10~4  normal  solution  the  conductance  correction 
amounts  to  0.18%.  That  the  hydrolysis  of  salts  of  the  weaker  bases 
becomes  appreciable  at  higher  temperatures  is  indicated  by  the  work 
of  Noyes  and  Melcher  4  with  the  salts  of  silver  and  of  barium.  In  the 
case  of  silver  nitrate,  at  higher  temperatures,  a  deposit  of  silver  was 
formed  over  the  inner  walls  of  the  platinum-lined  bomb.  This  pre- 
sumably was  the  result  of  a  precipitation  of  silver  oxide,  which  is  unstable 
at  these  temperatures  and  decomposes  to  metallic  silver  and  oxygen. 

The  extent  of  the  hydrolysis  of  salts  of  strong  acids  and  bases  is  very 
uncertain.  At  the  higher  concentrations,  these  electrolytes  appear  to  be 
ionized  somewhat  more  strongly  than  typical  salts.  Washburn  has  de- 
duced the  value  of  0.02  as  the  limit  approached  by  the  ionization  con- 
stant of  potassium  chloride  at  low  concentrations.  But  this  value  really 

"  Bottger,  Ztschr.  }.  phys.  Chem.  46,  602~(1903). 
« Noyes,  Carnegie  Publication,  No.  63,  p.  94, 


HOMOGENEOUS  IONIC  EQUILIBRIA  229 

represents  an  upper  limit  and  it  is  possible  that  the  true  value  may  be 
much  below  this  limit.  The  high  value  of  the  ionization,  however,  ren- 
ders any  precise  determination  of  the  limiting  value  of  the  mass-action 
function  uncertain,  and,  indeed,  if  conductance  data  alone  are  considered 
it  is  even  uncertain  that  a  definite  limit  greater  than  zero  is  approached.4* 
The  strong  acids  and  strong  bases  are  ionized  to  practically  the  same 
extent  at  higher  concentration ;  and  if  the  ionization  functions  in  the  case 
of  these  two  types  of  electrolytes  approach  the  same  limits  at  low  con- 
centrations, the  conductance  of  a  salt  as  measured  will  be  found  some- 
what lower  than  the  true  value  if  hydrolysis  becomes  appreciable.  On 
the  other  hand,  if  the  functions  of  acid  and  of  base  approach  values  which 
differ  considerably,  then  the  result  will  be  to  increase  the  conductance  of 
the  solution  above  that  of  the  unhydrolyzed  salt.  If,  for  example,  the 
ionization  constant  of  the  acid  relative  to  that  of  the  base  were  10~3, 
then,  at  a  salt  concentration  of  10~5  N,  the  hydrolysis  would  have  a  value 
of  0.95  X  10"3  or  approximately  0.1  per  cent,  which  would  raise  the  con- 
ductance of  the  solution  approximately  0.3  per  cent.  In  view  of  the 
entire  lack  of  experimental  data  relating  to  the  limiting  values  of  the 
ionization  constants  of  the  strong  acids  and  bases,  conductance  measure- 
ments with  salts  at  concentrations  below  10~*  normal  cannot  be  inter- 
preted with  certainty. 

In  solutions  of  salts  of  weaker  acids  and  bases,  hydrolytic  equilibria 
appear  to  be  fairly  well  established.  This  lends  support  to  the  view  that 
the  ionization  constants  of  the  weaker  acids  and  bases,  as  well  as  that 
of  water,  are  not  materially  affected  by  the  presence  of  larger  amounts 
of  salt.  The  agreement  of  the  values  for  the  ionization  constant  of 
water  as  determined  from  a  measurement  of  the  conductance  of  solutions 
of  salts  of  weak  acids  and  bases,  with  that  as  determined  by  other 
methods,  indicates  that  the  fundamental  assumptions  underlying  the 
theory  of  hydrolytic  equilibria  are  substantially  correct.  In  these  equi- 
libria, the  ionization  of  the  salt  is  involved.  If,  as  some  assume,  the 
salts  are  completely  ionized  at  all  concentrations,  then  the  ionization  y 
of  the  salt  should  vanish  from  the  hydrolysis  equation,  which  would 
materially  affect  the  values  obtained  for  the  ionization  constant  of  water. 
At  the  present  time,  however,  data  making  such  a  comparison  possible 
are  not  sufficiently  precise  to  enable  us  to  draw  any  certain  conclusions. 

Among  other  typical  equilibria  involving  electrolytes  are  those  in 
which  a  strong  acid  or  a  strong  base  is  partitioned  between  two  weaker 

"  Naturally,  if  this  view  were  adopted,  it  would  be  necessary  to  recast  our  notion* 
relative  to  the  nature  of  electrolytic  equilibria. 


230        PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

bases  or  Weaker  acids.5  A  considerable  number  of  equilibria  of  this  type 
have  been  investigated  and,  in  general,  the  results  confirm  the  assump- 
tion that  the  strong  base  or  acid  is  distributed  between  the  weaker  acids 
or  bases  in  conformity  with  the  law  of  mass-action. 

Equilibria  similar  to  hydrolytic  equilibria  in  aqueous  solutions  have 
been  found  to  exist  in  solutions  in  non-aqueous  solvents.  Such  equi- 
libria are  to  be  expected  in  the  case  of  all  distinctly  acid  solvents  which 
are  capable  of  yielding  a  hydrogen  ion.  This,  therefore,  includes  solu- 
tions in  all  acids,  such  as  hydrocyanic  acid,  formic  acid,  acetic  acid,  etc. 
It  likewise  includes  solutions  in  hydrogen  derivatives  whose  acid  prop- 
erties are  extremely  weak,  such  as  ammonia,  for  example. 

Franklin6  has  shown  that  equilibria  of  the  hydrolytic  type  exist  in 
solutions  in  liquid  ammonia.  In  the  case  of  salts  of  very  weak  bases, 
such  as  mercury  for  example,  ammono-basic  salts  are  precipitated  when 
the  neutral  salt  is  dissolved.  These  precipitates  are  redissolved  on  the 
addition  of  an  acid,  while  precipitation  is  facilitated  by  the  addition  of 
an  ammono-base,  such  as  potassium  amide.  While  equilibria  of  the 
hydrolytic  type  thus  exist  in  ammonia  solutions,  the  evidence  indicates 
that  it  is  only  in  the  case  of  extremely  weak  bases  that  hydrolysis  takes 
place  to  an  appreciable  extent.  The  concentration  of  hydrogen  ions  in 
ammonia  is  without  doubt  of  an  exceedingly  low  order.  This  is  indicated 
by  the  fact  that  salts  whose  ammono-bases  are  practically  insoluble  in 
liquid  ammonia,  such  as  calcium  and  barium  nitrates,  for  example,  yield 
clear  solutions  when  dissolved  in  ammonia,  even  at  high  concentrations. 
Furthermore,  as  is  well  known,  solutions  of  the  alkali  metals,  as  well  as 
of  metals  of  the  alkaline  earths,  in  liquid  ammonia,  are  comparatively 
stable.  It  is  to  be  expected  that  such  would  not  be  the  case  if  the  con- 
centration of  tjhe  hydrogen  ions  were  appreciable. 

Schlesinger7  has  shown  that  solutions  of  salts  in  formic  acid  are 
appreciably  hydrolyzed.  He  found  that  on  passing  a  current  of  air 
through  solutions  of  chlorides  in  formic  acid  free  hydrochloric  acid  is 
carried  over.  That  hydrolysis  may  occur  in  solutions  in  other  solvents, 
such  as  hydrocyanic  acid,  for  example,  is  indicated  by  the  high  value  of 
the  residual  specific  conductance  of  the  pure  solvents.  It  is,  of  course, 
possible  that  in  these  cases  the  conductance  is  in  a  measurable  degree 
due  to  the  presence  of  impurities,  but  the  high  value  obtained  in  many 
instances  is  probably  due  to  the  presence  of  hydrogen  ions.  It  is  prob- 
able, moreover,  that  the  higher  the  dielectric  constant  of  the  medium,  the 
greater  the  concentration  of  hydrogen  ions  due  to  the  solvent.  No 

•Thiel  and  Roemer,  Ztschr.  f.  phys.  Ohem.  61,  114  (1908). 
•Franklin,  J.  Am.  Chem.  8oc.  £7,  820  (1905). 
» Schlesinger,  J.  Am.  Chem.  Soc.  33,  1932  (1911). 


HOMOGENEOUS  IONIC  EQUILIBRIA  231 

systematic  study-  has  been  made  of  reactions  of  the  hydrolytic  type  in 
non-aqueous  solvents. 

Certain  solvents,  such  as  sulphur  dioxide,  acetone  and  bromine,  for 
example,  appear  to  be  of  a  non-polar  type.  In  these  cases  it  is  to  be 
expected  that  equilibria  of  the  hydrolytic  type  do  not  exist.  In  the  case 
of  polar  solvents,  however,  we  may  expect  equilibria  of  the  hydrolytic 
type  even  though  hydrogen  ions  are  not  involved.  Mercuric  chloride 
may  serve  as  an  example  of  this  type  of  solvents.  This  salt,  when  fused, 
dissolves  typical  binary  salts  and  yields  solutions  which  conduct  the 
current  with  considerable  facility.  If  a  salt  of  the  type  of  potassium 
nitrate,  for  example,  were  dissolved  in  mercuric  chloride,  reaction  might 
be  expected  to  take  place,  with  the  formation  of  potassium  chloride  and 
mercuric  nitrate  in  the  solution.  This  reaction  is  obviously  of  the  hydro- 
lytic type.  Indeed,  we  see  that  reactions  of  the  type  MX  +  NY  = 
NX  +  MY,  which  take  place  in  mixtures  of  fused  salts,  are  of  the 
hydrolytic  type.  We  have  here,  however,  an  extreme  case  in  that,  in  all 
likelihood,  the  ionization  of  the  solvent  itself  is  extremely  high,  whereas 
in  the  case  of  ordinary  hydrolytic  reactions  the  ionization  of  the  solvent 
is  exceedingly  low.  There  is  reason  for  believing  that  examples  exist  of 
equilibria  of  the  hydrolytic  type  intermediate  between  those  of  water 
and  those  of  mixtures  of  fused  salts. 


Chapter  X. 

Heterogeneous  Equilibria  in  Which  Electrolytes 
Are  Involved. 

1.  The  Apparent  Molecular  Weight  of  Electrolytes  in  Aqueous  Solu- 
tion. If  an  electrolyte  is  dissolved  in  a  solvent  in  equilibrium  with  a 
second  phase,  the  thermodynamic  potential  of  the  solvent  is  displaced, 
and  a  displacement  in  equilibrium  results.  On  the  addition  of  an  elec- 
trolyte to  water,  therefore,  we  should  expect  a  change  in  the  solubility 
of  substances  in  this  solvent;  or,  in  case  water  itself  appears  as  a  second 
phase,  we  should  expect  a  displacement  in  the  freezing  point,  boiling 
point,  etc. 

The  earlier  experiments  on  the  freezing  point  of  aqueous  salt  solutions 
indicated  a  fairly  close  agreement  between  the  ionization  as  determined 
by  conductance  measurements  and  that  as  determined  from  freezing  point 
measurements.  These  data  have  been  examined  and  collected  by  Noyes 
and  Falk.1  In  solutions  of  the  binary  salts  the  agreement  is,  on  the 
whole,  fairly  close  in  dilute  solutions,  although  in  the  more  concentrated 
solutions  deviations,  which  exceed  possible  experimental  errors,  make 
their  appearance.  In  solutions  of  potassium  chloride  the  two  methods 
yield  practically  identical  results  up  to  concentrations  as  high  as  0.1 
normal. 

In  order  to  calculate  the  molecular  weight  of  a  substance  from  the 
freezing  point  of  its  solution,  the  laws  governing  the  equilibrium  in  the 
mixture  must  be  known.  Since  the  general  case  has  been  worked  out 
only  for  dilute  solutions,  it  is  obvious  that  the  ionization  of  electrolytes, 
and  the  molecular  condition  of  substances  in  general,  may  not  be  deter- 
mined from  freezing  point  determinations  at  higher  concentrations. 
Washburn  and  Maclnnes2  showed  that,  while  the  freezing  point  curve 
for  potassium  chloride  corresponds  very  nearly  with  that  of  a  solution 
of  sugar  in  water  up  to  fairly  high  concentrations,  those  for  solutions  of 
lithium  chloride  and  caesium  nitrate  exhibit  deviations  at  fairly  high 
dilutions.  The  deviations  in  the  case  of  the  last  named  salts  lie  in  oppo- 
site directions  from  the  theoretical  curve  of  ideal  solutions.  They  found, 

1  Noyes  and  Falk,  J.  Am.  C hem.  8oc.  S3,  1437   (1911). 
'Washburn  and  Maclnnes,  J.  Am.  Chem.  Soc.  33,  1686   (1911). 

232 


HETEROGENEOUS  EQUILIBRIA  233 

however,  that  at  lower  concentrations  the  curves  for  the  three  salts  ap- 
proach that  of  an  ideal  system,  assuming  the  ionization  to  be  given  by 

the  conductance  ratio  -T-. 

Ao 

More  recently  the  methods  for  determining  the  temperature  of  solu- 
tions in  equilibrium  with  ice  have  been  greatly  refined,  and  molecular 
weight  determinations  are  available  at  very  low  concentrations.  In 
Table  LXXXVI,  under  ^  are  given  values  of  the  ionization  for  potassium 

chloride  at  low  concentrations  as  determined  by  Adams 3  and  by  Bed- 
ford.4 Under  yc  are  given  values  of  the  ionization  at  the  same  concen- 
trations as  determined  from  conductance  measurements. 

TABLE  LXXXVI. 

COMPARISON  OF  THE  IONIZATION  VALUES  FOR  POTASSIUM  CHLORIDE  FROM 
FREEZING  POINT  AND  CONDUCTANCE  MEASUREMENTS. 

C  X  103          Yi  (Adams)       y^  (Bedford)  yc 

2  0.969  ....  0.971 

5  0.961  0.959  0.956 

10  0.943  0.939  0.941 

20  0.922  0.915  0.922 

50  0.888  ....  0.889 

100  0.861  ....  0.860 

An  examination  of  this  table  shows  that  the  ionization  values  as  deter- 
mined by  the  freezing  point  method  correspond  within  the  limits  of  error 
with  those  as  determined  by  the  conductance  method.  The  temperature  of 
the  conductance  measurements,  in  this  case,  was  18°,  while  that  of  the 
freezing  point  measurements  was  necessarily  in  the  neighborhood  of  0°. 
It  is  known,  however,  that  at  fairly  high  dilutions  the  ionization  of  salts 
varies  only  little  between  .0°  and  18°.  The  results  are  therefore  com- 
parable. 

In  Table  LXXXVII  are  given  values  of  the  ionization  as  determined 
from  freezing  point  and  conductance  measurements  for  solutions  of  potas- 
sium nitrate,  potassium  iodate,  sodium  iodate,  and  for  equi-molar  mix- 
tures of  potassium  chloride  and  potassium  nitrate,  and  potassium  iodate 
and  sodium  iodate.5 

Examining  the  results  given  in  the  following  table,  it  is  evident  that, 
in  the  case  of  potassium  nitrate,  the  ionization  values  by  the  two  methods 

•Adams,  J.  Am.  Chem.  Soc.  37,  482  (1915). 

*  Bedford,  Proc.  Roy.  Soc.  (A)  83,  454   (1910). 

•  Hall  and  Harkins,  J.  Am.  Chem.  Soc.  S8,  2658  (1916). 


234        PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 


TABLE  LXXXVII. 

COMPARISON  OF  THE  IONIZATION  VALUES  OF  SALTS  AS  DERIVED  FROM 
FREEZING  POINT  AND  CONDUCTANCE  MEASUREMENTS. 

Potassium  Nitrate 
C  X  103  Yi  (Adams)  Yc 

2  0.967  0.970 

5  0.958  0.953 

10  0.937  0.935 

20  0.908  0.911 

50  0.848  0.867 

100  0.787  0.824 

I 
Potassium  lodate 

C  X 103  Y;  (Hall  &  Harkins)  YC 

2  0.940  0.965 

5  0.929  0.946 

10  0.916  0.928 

20  0.890  0.903 

50  0.835  0.860 

100  0.764  0.819 

Sodium  lodate 
C  X  103  Y;  (Hall  &  Harkins)  YC 

2  0.950  0.960 

5  0.934  0.939 

10  0.915  0.917 

20  0.890  0.890 

50  0.832  0.842 

100  0.772  0.801 

Equal  Molecular  Mixtures  of  KCl  and  KNOS 
C  X  103  Y;  (Hall  &  Harkins) 

10  1.94 

20  1.914 

50  1.868 

100  1.827 

200  1.773 

Equal  Molar  Mixtures  of  KI03  and  NaI03 
C  X  103  Y-  (Hall  &  Harkins) 


10 

20 

50 

100 


1.912 
1.890 
1.834 
1.768 


HETEROGENEOUS  EQUILIBRIA 


235 


agree  at  concentrations  below  20X10"3  N.  At  higher  concentrations,  how- 
ever, the  freezing  point  method  yields  lower  values  than  the  conductance 
method.  In  the  case  of  potassium  iodate,  the  agreement  is  not  so  good. 
At  the  lower  concentrations  the  value  of  the  ionization  as  determined  by 
the  conductance  methods  is  about  1.5  per  cent  higher  than  that  deter- 
mined by  the  freezing  point  method.  The  limiting  value  of  the  conduct- 
ance of  the  iodates  is  much  less  certain  than  is  that  of  the  chlorides  and 
'nitrates,  and  it  is  possible  that  the  ionization  values,  as  determined  by 
this  method  are  in  error  owing  to  an  error  in  the  value  of  A0.  If  the 
value  of  A0  were  increased  by  1.5  per  cent,  the  conductance  values  for 
potassium  iodate  would  agree  up  to  a  concentration  of  0.05  normal.  In 
solutions  of  sodium  iodate,  the  discrepancies  exceed  the  limit  of  experi- 
mental error,  of  the  conductance  measurements,  at  any  rate.  It  is  pos- 
sible that  here,  also,  an  error  in  the  value  of  A0  would  tend  to  harmonize 
the  results. 

As  regards  the  freezing  point  of  equi-molar  mixtures  of  two  electro- 
lytes, it  is  interesting  to  note  that  the  values  of  i  for  the  mixtures  are 
practically  the  mean  of  those  for  the  pure  substances  at  the  same  concen- 
tration. 

In  Table  LXXXVIII  are  given  values  of  i  for  salts  of  higher  type,6 
together  with  values  of  y^  and  Yc»  where  reliable  values  of  Y  ars 
available. 

TABLE    LXXXVIII. 

IONIZATION  OP  SALTS  OF  HIGHER  TYPE  AS  DETERMINED  BY  THE  FREEZING 
POINT  AND  CONDUCTANCE  METHODS. 

CX103    i  (Hall  &  Harkins)    y-  (Hall  &  Harkins)         ~ 


5 

10 

20 

50 

100 

200 

500 

5 

10 

20 

50 

100 

200 


Magnesium  Sulphate,  MgS04 


1.708 
1.614 
1.520 
1.394 
1.303 
1.214 
1.099 


0.708 
0.614 
0.520 
0.394 
0.303 
0.214 
0.099 


Potassium  Sulphate,  K2S04 

2.830  0.915 

2.772  0.886 

2.701  0.851 

2.567  0.784 

2.451  0.726 

2.327  0.664 


0.741 
0.669 
0.596 
0.506 
0.449 
0.403 


0.905 
0.872 
0.832 
0.771 
0.722 
0.673 


•Hall  and  Harkins,  loc.  cit. 


236        PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

Barium  Chloride,  BaCl2 

5  2.847  0.924  

10  2.790  0.895  0.883 

20  2.730  0.865  0.850 

50  2.647  0.824  0.798 

100  2.585  0.793  0.759 

200  2.535  C.768  0.720 

Cobalt  Chloride,  CoCl2 

5  2.858  0.929 

10  2.802  0.901 

20  2.749  0.875 

50  2.687  0.844 

Lanthanum  Nitrate,  La(N03)z 

5  3.694  0.898  

10  3.578  0.859  0.802 

20  3.440  0.813  

50  3.261  0.754  0.701 

100  3.149  0.716  

200  3.063  0.688  

500  3.002  0.667  

The  agreement  between  the  ionization  values  as  determined  from 
conductance  and  freezing  point  measurements,  in  the  case  of  the  salts  of 
higher  type,  is  not  as  close  as  in  that  of  the  binary  salts.  The  devia- 
tions in  the  more  dilute  solutions  are  in  the  neighborhood  of  one  per  cent, 
for  the  uni-divalent  salts.  In  solutions  of  potassium  sulphate  the  ioniza- 
tion values  by  the  freezing  point  method  are  slightly  higher  than  those 
by  the  conductance  method,  except  at  a  concentration  of  0.2  normal, 
where  the  conductance  method  gives  a  slightly  higher  value.  On  the 
whole,  for  this  salt  the  agreement  is  fairly  close  and  it  is  possible  that 
the  discrepancies  which  remain  may  be  due  to  error  in  the  value  of  A0 
employed.  In  the  case  of  barium  chloride,  the  ionization  values  by  the 
freezing  point  method  at  the  lower  concentrations  are  slightly  over  one 
per  cent  higher  than  those  by  the  conductance  method.  At  the  higher 
concentration  the  difference  in  the  values  increases  to  five  per  cent  at 
0.2  normal.  The  differences  at  the  lower  concentrations  may  arise  from 
uncertainties  in  the  values  of  A0,  but  at  the  higher  concentrations  there 
is  evidently  a  definite  divergence  between  the  two  curves.  Accurate  con- 
ductance values  for  cobalt  chloride  are  not  available.  The  values  of  i, 
however,  do  not  differ  greatly  from  those  of  barium  chloride  or  potassium 
sulphate. 

In  solutions  of  lanthanum  nitrate,  the  ionization  values  as  deter- 


HETEROGENEOUS  EQUILIBRIA  237 

mined  by  the  freezing  point  method  are  approximately  seven  per  cent 
greater  than  those  determined  by  the  conductance  method.  Comparison, 
however,  can  be  made  only  at  two  concentrations.  The  discrepancies 
in  the  values  appear  to  be  greater  than  might  be  expected  from  any 
possible  errors  in  the  assumed  value  of  A0.  In  the  case  of  magnesium 
sulphate,  there  is  a  marked  divergence  between  the  values  of  the  ioniza- 
tion  as  determined  by  the  two  methods.  However,  as  the  concentration 
decreases,  the  ionization  curves,  as  given  by  the  two  methods,  approach 
each  other. 

Considering  these  results  broadly,  it  may  be  concluded  that  the  freez- 
ing point  and  the  conductance  methods  give  values  for  the  ionization 
which  fall  very  nearly  within  the  limits  of  experimental  error  at  concen- 
trations approaching  10~3  normal  for  solutions  of  the  binary  salts,  and 
that  in  the  case  of  solutions  of  salts  of  higher  type  the  differences  between 
the  values,  as  determined  by  the  two  methods,  do  not,  in  general,  exceed 
one  per  cent  at  low  concentrations  for  salts  of  the  uni-divalent  type. 
For  salts  of  the  di-divalent  type,  the  discrepancies  between  the  values, 
as  determined  by  the  two  methods,  are  markedly  greater,  lying  in  the 
neighborhood  of  5  per  cent,  and  the  same  is  true  of  lanthanum  nitrate. 
In  general,  however,  in  the  case  of  salts  of  higher  type,  the  divergence 
of  the  values  determined  by  the  two  methods  diminishes  as  the  concen- 
tration decreases. 

Considering  the  results  of  freezing  point  determinations,  it  is  a  strik- 
ing fact,  the  significance  of  which  cannot  be  ignored,  that,  as  the  concen- 
tration decreases,  the  molecular  depression  of  the  freezing  point  increases 
and  approaches  a  limiting  value,  which,  in  the  case  of  salts  of  different 
types,  corresponds  with  the  ionic  structure  of  these  salts  and  which  is 
in  agreement  with  the  fundamental  ionic  reactions  assumed  by  the  ionic 
theory.  So  the  value  of  i  for  the  binary  salts  approaches  a  value  of  2,  for 
ternary  salts  3,  for  quaternary  salts  4,  etc.  While  the  significance  of  the 
agreement  between  the  results  of  freezing  point  and  conductance  meas- 
urements remains  uncertain,  the  fundamental  importance  of  the  fact  that 
the  limits  approached  in  the  two  cases  are  substantially  the  same  should 
not  be  overlooked. 

The  difference  between  the  results  by  the  two  methods  at  the  higher 
concentrations  are  readily  explainable,  since  the  calculation  of  the  num- 
ber of  molecules  present  in  a  mixture  is  based  upon  the  assumption  that 
the  laws  of  dilute  solutions  hold.  Even  in  the  case  of  non-electrolytes, 
the  laws  of  dilute  solutions  fail  to  hold  at  concentrations  as  low  as  0.1 
normal,  and  it  is  therefore  a  priori  probable  that  the  laws  of  dilute  solu- 


238        PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

tions  in  electrolytic  systems  will  fail  at  concentrations  below  this  value. 
Furthermore,  in  the  case  of  salts  of  higher  type,  it  is  not  improbable  that 
intermediate  ions  are  formed,  as  a  result  of  which  a  divergence  will  arise 
between  the  results  as  determined  by  conductance  and  by  osmotic 
methods. 

Nernst 7  has  called  attention  to  the  fact  that,  since  the  law  of  mass- 
action  in  its  simple  form  does  not  hold  for  solutions  of  strong  electrolytes, 
the  laws  of  dilute  solutions  cannot  be  applied  to  these  mixtures.  As  a 
consequence,  if  the  ionization  is  correctly  determined  by,  the  conductance 
method,  the  ionization  as  determined  by  osmotic  methods,  assuming  the 
laws  of  dilute  solutions  to  hold,  should  differ  from  that  determined  by 
conductance  measurements.  It  appears,  however,  that  in  the  case  of 
certain  electrolytes,  such  as  potassium  chloride,  osmotic  methods  and 
conductance  methods  lead  to  the  same  value  of  the  ionization,  and,  in 
the  case  of  other  electrolytes,  the  two  methods  lead  to  very  nearly  the 
same  value  at  concentrations  approaching  10~3  normal.  Yet,  in  the 
neighborhood  of  10~3  normal,  strong  electrolytes  do  not  conform  to  the 
simple  law  of  mass-action.  Those  who  would  use  the  results  of  osmotic 
methods  to  substantiate  the  correctness  of  the  results  of  conductance 
methods  thus  find  themselves  in  a  dilemma,  for,  if  the  two  methods  lead 
to  identical  values  of  the  ionization,  then,  if  the  results  of  osmotic  meas- 
urements are  looked  upon  as  correct,  the  interpretation  of  conductance 
measurements  must  be  in  error,  while,  if  the  results  of  conductance  meas- 
urements are  accepted  in  their  usual  sense,  the  laws  of  dilute  solutions 
are  inapplicable.  That  the  concordance  of  the  ionization  values  deter- 
mined by  conductance  and  osmotic  methods  at  low  concentrations  is  an 
accidental  one  is  very  improbable.  It  appears,  rather,  that  this  agree- 
ment is  the  expression  of  a  fundamental  property  of  such  solutions.  The 
significance  of  this  agreement,  however,  remains  uncertain.  This  ques- 
tion will  be  discussed  further  in  the  next  chapter. 

The  molecular  weight  of  electrolytes  in  aqueous  solutions  has  like- 
wise been  determined  from  the  measurement  of  the  elevation  of  the  boil- 
ing point.  The  precision  of  such  measurements  is  necessarily  much 
lower  than  that  of  the  freezing  point  depression  and  need  not  be  discussed 
in  detail  here.  The  molecular  weight  of  electrolytes  in  aqueous  solutions 
has  also  been  determined  from  vapor  pressure  measurements.8  The 
experimental  difficulties  attending  the  use  of  this  method  are  very  great 
and  it  is  doubtful  if  the  precision  of  such  determinations  equals  that  of 

T  Nernst,  Ztschr.  f.  pJiys.  Chem.  38,  494   (1901). 

"Lovelace,  Frazer  and  Sease,  J.  Am,  Chem.  SQC.  $3,  102  (1921). 


HETEROGENEOUS  EQUILIBRIA 


239 


the  freezing  point  method.  The  results  obtained  agree  well  with  those 
obtained  by  the  freezing  point  method.8* 

2.  The  Molecular  Weight  of  Electrolytes  in  Non-Aqueous  Solutions. 
A  great  many  measurements  have  been  made  of  the  molecular  weight  of 
electrolytes  in  various  non- aqueous  solvents.  With  a  few  exceptions, 
the  boiling  point  method  has  been  employed.  The  resulting  data  suffer, 
consequently,  from  the  inaccuracies  inherent  in  this  method.  Measure- 
ments at  low  concentrations  appear  to  be  entirely  lacking.  In  general, 
in  solvents  of  fairly  high  dielectric  constant,  where  the  ionization  is  com- 
parable with  that  in  water,  the  molecular  weights  as  determined  lie 
below  the  normal  values  and  indicate  ionization.  In  solvents  of  fairly 
low  dielectric  constant,  usually  below  20,  the  apparent  molecular  weight 
rarely  indicates  ionization  at  higher  concentrations. 

The  most  extensive  molecular  weight  determinations  in  a  non-aqueous 
solvent  have  been  made  by  Walden  and  Centnerszwer 9  with  solutions  in 
sulphur  dioxide.  In  Table  LXXXIX  are  given  values  of  the  van't  Hoff 
factor  i  for  various  electrolytes  dissolved  in  sulphur  dioxide  at  dilutions 
from  1  to  16  liters.  An  inspection  of  the  table  shows  that,  at  a  dilution 

TABLE  LXXXIX. 

VALUES  OP  i  FOR  ELECTROLYTES  DISSOLVED  IN  SULPHUR  DIOXIDE. 


1. 

2. 

3. 

4. 

5. 

6. 

7. 

8. 

9. 
10. 
11. 
12. 
13. 
14. 
15. 
16. 
17. 
18. 


KJ    .....................  0.42 

KCNS   ..................  0.41 

NaJ    ........................ 

NH4J  ...................  0.41 

NH4CNS    ................  0.29 

RbJ    ....................  0.52 

N(CH3)H3C1   ............  0.28 

N(CH3)2H2C1    ...........  0.87 

N(CH3)3HC1   ............  1.12 

N(CH3)4C1    ..............  1.16 

N(CH3)4Br   ..............  1.30 

N(CH,)4J  ...............  1.26 

N(C2H5)HSC1    ...........  0.43 

N(C2H5)2H2C1    ...........  0.70 

N(C2H5)3HC1    ...........  1.15 

N(C2H5)J   ..............  1.61 

N(C7H7)H3C1    ...........  0.44 

S(CH3)3J    ...............  0.84 


0.55 
0.49 
0.57 
0.53 
0.40 
0.61 
0.38 
0.79 
1.00 
1.08 
1.10 
1.20 
0.50 
0.69 
1.06 
1.39 
0.51 
0.97 


4 

0.63 
0.60 


8 

0.74 
0.68 


16 

0.86 
0.71 


0.64        0.71        0.82 


0.73 

0.82 

0.85 

0.49 

0.62 

0.81 

0.76 

0.82 

0.86 

0.99 

0.96 

0.96 

1.05 

1.03 

1.02 

1.01 

0.97 

0.95 

1.16 

1.18 

1.23 

0.62 

0.68 

0.71 

0.70 

0.76 

0.78 

1.06 

1.05 

1.06 

1.27 

1.17 

1.11 

0.59 

0.72 

0.80 

1.03 

1.06 

1.08 

••According  to  Heuse  (Thesis,  Univ.  of  111.,  1914),  the  agreement  between  the  con- 
ductance and  the  vapor  pressure  method  does  not  hold  for  KC1  at  25°.  .  See  also  Wash- 
burn,  "Principles  of  Physical  Chemistry,"  Ed.  2,  p.  268. 

•  Walden  and  Centnerszwer,  Ztschr.  /.  phys,  Chem,  39,  513   (1902), 


240        PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

of  16  liters,  a  few  salts  have  a  value  of  i  greater  than  unity,  while  the 
greater  proportion  of  the  salts  has  a  value  of  i  less  than  unity.  At 
higher  concentrations  the  curves  exhibit  a  very  complex  form.  In  the 
case  of  most  of  the  substances  which  have  a  relatively  high  value  of  i  at 
lower  concentrations,  the  value  changes  but  little  until  a  concentration 
of  0.2  normal  is  reached,  when  the  value  of  i  begins  to  increase  rapidly 
with  increasing  concentration.  In  the  case  of  salts  having  a  low  value  of 
i  at  the  lower  concentrations,  the  value  of  i,  in  general,  decreases  with 
increasing  concentration,  particularly  as  normal  concentration  is  ap- 
proached. Certain  of  the  electrolytes  exhibit  an  exceptional  behavior 
in  that  the  curves  of  the  i  values  intersect  those  of  the  majority  of  the 
electrolytes.  It  is  evident  that  molecular  weight  determinations  in  sul- 
phur dioxide  are  uncertain  in  their  significance.  On  the  whole,  the  curves 
exhibit  a  definite  trend  as  the  concentration  decreases  indicating  that  the 
value  of  i  will  ultimately  rise  above  unity.  It  is  to  be  borne  in  mind 
that  the  ionization  of  salts  in  sulphur  dioxide  is  relatively  low,  being  in 
general  less  than  20  per  cent  in  the  neighborhood  of  0.1  normal.  Further- 
more, even  in  the  case  of  aqueous  solutions,  freezing  point  and  con- 
ductance methods  lead  to  divergent  results  at  higher  concentrations.  If 
the  divergence  of  a  solution  of  an  electrolyte  from  the  simple  laws  of 
dilute  solutions  is  in  any  considerable  measure  due  to  the  electrostatic 
action  of  the  charged  particles  upon  one  another  or  upon  the  solvent  me- 
dium, then  it  is  to  be  expected  that  as  the  dielectric  constant  of  the  sol- 
vent is  smaller,  the  divergence  at  a  given  concentration  will  be  greater, 
since  the  force  due  to  a  charged  particle  varies  inversely  as  the  dielectric 
constant.  It  seems  not  improbable,  also,  that,  in  the  case  of  certain  sol- 
vents, polymerization  may  take  place  to  a  considerable  extent  at  higher 
concentrations.  This  would  greatly  complicate  the  behavior  of  these  solu- 
tions and  would  make  it  impossible  to  interpret  either  the  results  of 
conductance  or  of  osmotic  measurements. 

The  molecular  weights  of  a  number  of  electrolytes  in  liquid  ammonia 
at  its  boiling  point  have  been  determined  by  Franklin  and  Kraus 10  from 
the  boiling  point  measurements.  Owing  to  the  exceptionally  low  value 
of  the  boiling  point  constant  of  liquid  ammonia,  about  3.4,  measurements 
below  0.1  normal  were  not  made.  As  a  consequence,  the  determinations 
relate  almost  entirely  to  concentrations  at  which  it  might  be  expected  that 
the  laws  of  dilute  solutions  would  not  hold.  In  general,  in  the  neighbor- 
hood of  0.1  normal,  the  observed  elevation  of  the  boiling  point  corre- 
sponds approximately  with  a  normal  value  of  the  molecular  weight  of 
the  dissolved  electrolyte.  At  higher  concentrations,  the  molecular  eleva- 

»  Franklin  and  Kraus,  Am.  Chem.  J.  20,  836   (1898). 


HETEROGENEOUS  EQUILIBRIA  241 

tion  of  the  boiling  point  increases  in  the  case  of  all  the  salts  measured. 
It  is  obvious  that  in  these  solvents  the  concentration  at  which  the  meas- 
urements were  carried  out  is  too  high  to  admit  of  a  comparison  with 
the  results  of  the  conductance  method.  In  comparing  the  results  of  the 
conductance  method  with  that  of  other  methods  of  determining  the  degree 
of  ionization  of  salts  in  non-aqueous  solvents,  it  should  be  borne  in  mind 
that,  according  to  conductance  measurements,  the  deviations  from  the 
law  of  simple  mass-action  increase  greatly  as  the  dielectric  constant  of 
the  medium  decreases.  If,  then,  the  deviations  from  the  laws  of  dilute 
solutions  lead  to  a  lack  of  correspondence  between  the  results  of  the 
osmotic  and  the  conductance  methods,  the  discrepancy  between  the  results 
of  the  two  methods  should  be  the  greater,  the  greater  these  deviations. 
It  might  be  expected,  therefore,  that,  in  solvents  of  low  dielectric  con- 
stant, the  discrepancies  would  prove  to  be  very  great. 

In  solvents  of  fairly  high  dielectric  constant,  molecular  weight  deter- 
minations by  osmotic  methods  yield  values  for  the  ionization  which  are 
comparable  with  those  resulting  from  conductance  measurements,  and 
the  ionization  increases  as  the  concentration  decreases.  In  making  such 
comparisons,  however,  it  should  be  borne  in  mind,  not  only  that  the  ex- 
perimental errors  are  great  in  the  osmotic  determinations,  but,  also,  that 
the  conductance  values  are  more  or  less  uncertain,  and  that  the  values 
of  A0  are  often  subject  to  considerable  errors.  In  the  following  table  are 
given  values  of  the  ionization  YC  as  determined  from  conductance  meas- 
urements and  Y£  as  determined  from  the  elevation  of  the  boiling  point 
for  solutions  of  (C2H5)4NI  in  a  number  of  solvents.11 

TABLE  XC. 
VALUES  OF  i  FOR  SOLUTIONS  IN  DIFFERENT  SOLVENTS. 

CH3OH  CH3CN 

V  3  6  12  V  10  15 

Tc    0.38        0.45  0.52  YC  0.48  0.54 

yb    0.24        0.29  0.38  y&  0.49  0.57 

C2H5OH  C2H8CN 

V  30  V  30 

Yc     0.41  YC    0.53 

Y6    0.30  Y&     0.54 

"Walden,  Zttchr.  }.  phys.  Chem.  55,  281  (1906). 


242        PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

While  the  correspondence  between  the  two  methods  is  not  very  exact, 
nevertheless  it  is  evident  that  the  relations  in  these  solvents  are  similar 
to  those  found  in  aqueous  solutions. 

In  pyridine  the  values  of  i  are  in  general  less  than  unity,  as  may  be 
seen  from  the  following  table. 

TABLE  XCI. 

VALUES  OF  i  FOR  SOLUTIONS  IN  PYRIDINE. 
AgN03  (C2H5)4NI 

V=  128  7=   16  32 

i— 0.77        0.75        0.91  i—  0.73        0.82 

The  molecular  weight  of  sodium  iodide  in  acetone  has  been  deter- 
mined by  McBain  and  Coleman.12  The  values  obtained  are  very  nearly 
normal  from  0.9  to  0.04  normal  concentrations.  If  anything,  the  mole- 
cular weights  are  slightly  larger  at  the  lower  concentrations.  At  these 
concentrations,  the  conductance  method  indicates  an  ionization  varying 
from  17  to  43  per  cent.  It  is  evident  that  in  this  solvent  the  results  of 
conductance  and  of  osmotic  measurements  are  not  in  agreement.  In 
acetone,  however,  the  deviations  from  the  law  of  simple  mass-action  are 
large,  and  there  is  evidence  that  polymerization  of  the  dissolved  salts 
takes  place,  presumably  with  the  formation  of  complex  ions.12a  This 
renders  the  interpretation  of  results  in  the  more  concentrated  solutions 
difficult. 

Phenol  is  the  only  non-aqueous  solvent  in  which  the  molecular  weights 
of  salts  have  been  determined  at  relatively  low  concentration.  Riesen- 
feld,13  from  the  freezing  point  of  a  saturated  solution  of  potassium  iodide 
in  phenol,  whose  concentration  is  0.0045  normal,  obtained  a  value  of  170, 
for  the  molecular  weight  of  potassium  iodide,  which  corresponds  closely 
with  the  normal  value  of  166.  The  equivalent  conductance  of  solutions 
of  potassium  iodide  in  phenol  at  these  concentrations  is  of  the  order  of 
1.0.  Hartung14  has  measured  the  molecular  weights  of  a  number  of 
salts  in  phenol  by  the  freezing  point  method.  These  include  tetramethyl- 
ammonium  iodide,  sodium  acetate,  aniline  hydrochloride,  dimethylamine 
hydrochloride,  as  well  as  several  organic  salts  of  alkali  metals.  The 
concentrations  run  to  dilutions,  in  some  cases,  as  low  as  0.01  normal.  In 
the  following  table  are  given  the  values  obtained  for  i  for  solutions  of 
tetramethylammonium  iodide  and  sodium  acetate  in  phenol.  With 
aniline  hydrochloride,  i  has  a  value  of  unity  at  a  concentration  of  0.02  N 

"McBain  and  Coleman,  Trans.  Faraday  Soc.  15.  45   (1919). 
"•Serkov,  Ztschr.  f.  phys.  Chem.  78,  567   (1910). 
«  Riesenfeld,  Ztschr.  /.  phys.  Chem.  41.  346  (1902). 
"Hartung,  Ztschr.  /.  phys.  Chem.  77,  82  (1911). 


HETEROGENEOUS  EQUILIBRIA  243 

and  decreases  to  values  less  than  unity  at  higher  concentrations.  In  the 
case  of  dimethylamine  hydrochloride  i  has  a  value  of  1.18  at  V  =  23, 
and  decreases  to  a  value  in  the  neighborhood  of  unity  at  a  dilution  of 

TABLE  XCII. 
MOLECULAR  WEIGHTS  OF  SALTS  IN  PHENOL. 


Tetramethylammonium  Iodide.           M  = 

201.1 

V 

M(obs.) 

t 

92.7 

135.5 

1.48 

38.9 

143.5 

1.40 

22.9 

150.2 

1.34 

12.3 

163.9 

1.23 

8.18 

171.5 

1.17 

5.70 

177.6 

1.13 

4.75 

182.6 

1.10 

4.08 

185.4 

1.08 

3.52 

188.8 

1.07 

3.05 

189.0 

1.06 

2.67 

190.0 

1.05 

2.40 

191.1 

1.05 

2.10 

191.5 

1.06 

1.73 

188.9 

1.07 

1.59 

185.3 

1.08 

Sodium  Acetate.        M  =  82.1 

V 

M(obs.) 

t 

41.8 

46.6 

1.75 

29.5 

48.8 

1.66 

20.5 

54.0 

1.51 

16.3 

57.5 

1.43 

13.3 

59.9 

1.37 

11.4 

61.8 

1.33 

9.68 

63.5 

1.30 

8.70 

65.0 

1.27 

7.62 

66.5 

1.23 

6.86 

67.1 

1.22 

5.89 

68.0 

1.20 

5.12 

69.5 

1.19 

4.43 

70.2 

1.16 

3.85 

72.0 

1.14 

3.37 

73.5 

1.11 

2.98 

76.7 

1.06 

2.65 

78.4 

1.04 

2.37 

81.0 

1.01 

2.15 

82.9 

0.99 

2.0 

83.0 

0.99 

244        PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

2  liters.  As  may  be  seen  from  the  table,  the  value  of  i  for  tetramethyl- 
ammonium  iodide  in  the  neighborhood  of  0.01  N  is  approximately  1.50, 
while  that  for  sodium  acetate  is  even  higher  than  that  of  tetramethyl- 
ammonium iodide,  being  1.75  at  V  =  41.8. 

Phenol  has  a  dielectric  constant  of  9.68  and  the  high  values  obtained 
for  i  are  unexpected.  The  conductance  of  solutions  of  tetramethylam- 
monium  iodide  in  phenol  at  45°  has  been  measured  by  Kurtz.14a  The 
constants  for  these  solutions  are  m  =  1.28,  D  =  0.69,  K  =  2.3  X  10~* 
and  A0  =  16.67.  Solutions  of  tetramethylammonium  iodide  in  phenol 
thus  exhibit  an  ionization  not  very  different  from  that  found  for  solutions 
of  typical  salts  in  other  solvents,  having  a  dielectric  constant  in  the 
neighborhood  of  10.  While  the  ionization  is  marked  at  the  lower  con- 
centrations, the  value  is  much  lower  than  corresponds  to  the  value  of  i 
found  by  Hartung.  Thus,  at  a  concentration  0.01  N,  the  ionization  from 
the  conductance  values  is  0.194  in  contrast  to  0.48  from  freezing  point 
determinations. 

It  is  evident  that  there  is  a  wide  discrepancy  between  the  values  of 
the  ionization  as  determined  by  the  two  methods.  It  is  particularly 
striking  that  the  values  of  i  found  for  salts  of  weak  organic  acids  are 
higher  than  those  for  typical  electrolytes.  Since  phenol  is  an  acid  sol- 
vent, it  is  probable  that  a  solvolytic  reaction  takes  place  when  a  salt  is 
dissolved  in  phenol  according  to  the  equation: 

PhOH  +  MX  =  MOPh  +  HX. 

If  this  were  the  case,  we  should  expect  the  greatest  values  of  i  in  the 
case  of  salts  of  weak  acids  and  bases,  which  would  account  for  the  high 
values  found  for  solutions  of  tetramethylammonium  iodide  and  sodium 
acetate.  Lacking  further  experimental  material,  however,  the  question 
must  be  left  open. 

The  results  obtained  from  molecular  weight  determinations  indicate 
that,  in  solvents  of  intermediate  dielectric  constant,  the  values  of  y^ 
approach  those  of  yc  at  low  concentrations.  At  high  concentrations  the 

divergence  is  often  great  and  the  variation  of  the  i  values  depends  greatly 
on  the  nature  of  the  electrolyte.  In  solvents  of  dielectric  constant  lower 
than  20,  the  values  of  y  by  the  two  methods  are  not  in  agreement.  This 
is  not  surprising,  since  these  solutions  may  be  expected  to  show  large 
divergences  from  the  laws  of  ideal  systems.  So  far  as  may  be  judged 
from  the  available  material,  however,  at  very  low  concentrations,  y  •  and 

7_   approach  a   common  limit   in  non-aqueous   solutions.     The  corre- 
i/ 

"a  Kurtz,  Thesis,  Clark  Univ.   (1920). 


HETEROGENEOUS  EQUILIBRIA  245 

spondence  found  between  the  values  of  y^  and  Yc  m  aqueous  solutions 

appears,  therefore,  to  be  a  property  of  electrolytic  solutions  in  other 
solvents  also. 

3.  Solubility  of  Non-Electrolytes  in  the  Presence  of  Electrolytes. 
The  solubility  of  non-electrolytes  in  water  is,  in  the  majority  of  cases, 
depressed  by  the  addition  of  an  electrolyte.  The  effect  of  the  added 
electrolyte  on  the  solubility  depends  upon  the  nature  of  the  substance  in 
question,  as  well-  as  upon  that  of  the  added  electrolyte.  If  reaction  takes 
place  between  the  two,  the  solubility  is  naturally  influenced  by  this 
reaction. 

For  certain  substances,  the  solubility  is  very  nearly  a  linear  function 
of  the  concentration  of  the  added  salt,  in  which  case  it  may  be  expressed 
by  the  equation: 

(62)  S  =  S0  +  BS0C 

where  S0  is  the  solubility  of  the  non-electrolyte  in  pure  water,  S  is  the 
solubility  in  the  presence  of  the  salt  at  the  concentration  C,  and  B  is  the 
solubility  coefficient,  which  is  a  constant  if  the  solubility  varies  as  a 
linear  function  of  the  concentration.  In  general,  however,  the  solubility 
function  is  not  a  linear  one.  The  change  in  the  solubility  for  a  given 
addition  of  electrolyte  is,  as  a  rule,  the  greater  the  smaller  the  amount  of 
electrolyte  added.  The  solubility  is  more  accurately  expressed  by  the 
equation: 

q 

.(63)  log  -=-  =  PC,15  where  p  is  a  constant. 

O0 

In  the  following  table  are  given  values  for  the  solubility  of  hydrogen 
in  aqueous  solutions  of  different  electrolytes.18  In  pure  water,  the  solu- 

TABLE   XCIII. 

SOLUBILITY  OF  HYDROGEN  IN  AQUEOUS  SOLUTIONS  OF  ELECTROLYTES  AT 
DIFFERENT  CONCENTRATIONS  AT  25°. 

C=                           0.5               1  2  3  4 

CH3COOH   .........  0.0192  .    0.0191  0.0188  0.0186        0.0186 

CH,C1COOH    ......  0.0189        0.0186  0.0180  ........ 

HN03   .............  0.0188        0.0183  0.0174  0.0167        0.0160 

HC1    ...............  0.0186        0.0179  0.0168  0.0159  ____ 

H2°4   .............     0.0185        0.0177        0.0163        0.0150        0.0141 


KOH  ..............     0.0167        0.0142          ........ 

NaOH   .............     0.0165        0.0139        0.0097        0.0072        0.0055 

"Rothmund,    Ztschr.   f.   Electroch.   7,   675    (1901)  ;   Ztschr.   f.   phys.    Chem.   69,  524 
(1909)  ;  Nernst,  ibid.,  38,  494   (1901). 

"Geffcken,  Ztschr.  f.  phys.  Chem.  49,  257  (1904). 


246        PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 


bility  of  hydrogen  at  25°  is  0.01926.  The  results  are  shown  graphically 
in  Figure  48.  An  examination  of  the  table  shows  that  solubility  depres- 
sion is  a  specific  property  of  the  electrolyte.  The  depression  due  to 
chloroacetic  acid  is  slightly  greater  than  that  due  to  acetic  acid.  Nitric, 
hydrochloric  and  sulphuric  acids  cause  a  small,  but  markedly  greater, 
depression  of  the  solubility.  On  the  other  hand,  sodium  and  potassium 
hydroxides  cause  a  marked  depression  of  the  solubility. 

The  solubilities  may  be  compared  by  means  of  the  solubility  coeffi- 


o.ooo 


in         zn         3* 

Concentration  of  Added  Electrolyte. 


FIG.  48.    Solubility  of  Hydrogen  in  Water  at  25°  in  the  Presence  of  Electrolytes 

at  Varying  Concentrations. 

cient  for  the  percentage  equivalent  solubility  change,  as  defined  by  the 
equation : 


(64) 


B'  =  100 


S0  —  S 


X 


S0      ^  C' 

In  Table  XCIV  are  given  the  values  of  the  percentage  equivalent 
solubility  depression  of  hydrogen,  corresponding  to  Table  XCIII.  If 
the  solubility  varied  as  a  linear  function  of  the  concentration  of  the  salt, 
the  equivalent  percentage  solubility  depression  would  be  a  constant.  As 
may  be  seen  by  reference  to  Figure  48,  the  curves  are  convex  towards  the 
axis  of  concentrations,  which  corresponds  to  a  decrease  in  the  solubility 
coefficient.  In  Table  XCV  are  given  values  of  the  relative  percentage 
solubility  depression  for  nitrous  oxide  and  in  Table  XCVI  those  for 
oxygen  at  25°  and  15°.  It  will  be  observed,  in  the  first  place,  that  the 
percentage  solubility  effect  is  in  certain  cases  a  function  of  the  tempera- 


HETEROGENEOUS  EQUILIBRIA  247 

TABLE  XCIV. 

EQUIVALENT  PERCENTAGE  SOLUBILITY  DEPRESSION  FOR  HYDROGEN  IN 

WATER  AT  25°. 

C=  0.5  1  2  3  4 

CH3COOH 1.0  1.0  1.0             1.0 

CH2C1COOH   3.7%  3.4  3.3 

HN03   4.8  4.9  4.8  4.4              4.2 

HC1                                        7.3  7.0  6.4  5.8 


H2S04 


8.0  8.1  7.7  6.7 


2 

KOH   26.6  26.4 

NaOH   28.6  27.9  24.8  20.9  17.9 

TABLE    XCV. 

RELATIVE  PERCENTAGE  SOLUBILITY  DEPRESSION  OF  NITROUS  OXIDE 

AT  25°  AND  15.° 

t  =  25°  t  =  15° 


0.5        1         2         3        4         0.5        1         2         3         4 

HN03   ....— 1    —1    —1.1       ..      ..000 

HC1   +5.7  +  4.4  +  3.1       . .      . .     +  5.9  +  5.1  +4.0       . . 

H2^°4  ....      9.4      8.7      7.2      6.3     5.5       11.3     10.2      8.6      7.5      6.9 

NH4C1  ...  12.4  10.9       12.8  11.2       

CsCl    16.8  17.5 

KJ    17.8  17.2       19.5  18.6       

KBr   19.5  18.3       20.8  19.4       

LiCl   19.8  18.7       20.8  19.9       

RbCl 20.5  18.7       21.3  19.7       

KC1    20.6  20.0  ..        ..       ..  23.6  20.6       

KOH    ....  26.9  26.6       28.3  28.1       

TABLE  XCVI. 

RELATIVE  EQUIVALENT  PERCENTAGE  SOLUBILITY  DEPRESSION  OF  OXYGEN  AT  25°  AND  15°. 
t  =  25°  t  =  15° 


c  = 

0.5 

1 

2 

3 

4 

5 

0.5 

1 

2 

3 

4 

5 

HN03    .... 

4 

4 

4 

8.3 

7.4 

6.6 

HC1 

7.8 

6.8 

6.3 

10.4 

8.9 

1  0  fi 

in  7 

Q  A 

81 

7  K 

1  O  O 

1  A  *7 

n  n 

O  O 

O  O 

2 

lo.  U 

J.U./ 

9.4 

0.4 

.1 

7.5 

lo.8 

10.7 

9.9 

8.8 

8.0 

NaCl    

30.0 

27.6 

24.3 

^ 

30.3 

28.4 

25.1 

KsSO, 
2 

35.7 

32.8 

.. 

38.0 

34.7 

.. 

.. 

KOH 

36.4 

33.1 

397 

35.5 

NaOH  .... 

37.7 

33.8 

28.6 

.  . 

f  f 

,  . 

41.3 

36.4 

30.6 

t  m 

f  t 

f  f 

248        PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

ture,  while  in  other  cases  the  solubility  effect  is  relatively  independent  of 
temperature.  In  the  presence  of  nitric  acid,  the  coefficient  for  oxygen 
increases  from  4  to  8  per  cent,  as  the  temperature  falls  from  25°  to  15°. 
In  the  presence  of  hydrochloric  acid  the  coefficient  increases  slightly, 
while  in  the  presence  of  sulphuric  acid  the  coefficient  changes  but  little. 
In  the  presence  of  sodium  chloride,  the  coefficient  is  practically  identical 
at  the  two  temperatures.  The  solubility  of  nitrous  oxide  appears  to  vary 
less  than  that  of  oxygen  as  the  temperature  changes. 

The  order  of  the  electrolytes  in  terms  of  their  solubility  effect  is 
practically  the  same  for  different  gases.  Indeed,  in  many  cases,  the 
solubility  coefficients  for  different  gases  are  very  nearly  the  same  for  the 
same  electrolyte.  An  inspection  of  the  tables  will  show  that,  in  general, 
the  order  in  which  the  electrolytes  appear  is  the  same.  In  certain  cases, 
however,  the  solubility  effects  show  an  influence  due  to  the  nature  of  the 
dissolved  gas.  For  example,  in  a  1.0  normal  solution,  the  solubility 
coefficient  for  hydrogen  in  the  presence  of  nitric  acid  is  4.9,  that  of 
oxygen  is  4,  and  that  of  nitrous  oxide  is  —  1  per  cent.  The  negative  sign 
indicates  that  the  solubility  is  increased  on  addition  of  the  electrolyte. 
The  solubility  effect  is  smallest  in  the  case  of  the  acids  and  is  greatest  in 
that  of  the  bases.  The  solubility  coefficients  for  the  salts  are,  in  general, 
slightly  smaller  than  those  for  the  bases. 

In  Table 1T  XCVII  are  given  values  of  the  percentage  equivalent  solu- 
bility depression  for  a  variety  of  substances  in  the  presence  of  different 
electrolytes.  A  comparison  of  the  results  collected  in  this  table  shows 
that  the  order  of  electrolytes  as  regards  their  effect  on  the  solubility  of 
different  substances  is  practically  identical  throughout.  This  is  particu- 
larly true  in  the  case  of  those  substances  where  reaction  with  the -electro- 
lyte is  not  to  be  expected.  The  smallest  effect  for  typical  salts  is  ob- 
served in  the  case  of  ammonium  nitrate.  However,  any  general  relation 
between  the  nature  of  the  electrolyte  and  the  nature  of  the  solubility 
effect  cannot  be  established.  The  action  is  specific  in  character. 

With  a  few  exceptions,  the  addition  of  an  electrolyte  to  a  solution 
of  a  non-electrolyte  in  water  causes  a  depression  in  the  solubility  of  the 
non-electrolyte.  This  effect,  which  has  been  called  a  "salting  out" 
effect,  is  not,  however,  characteristic  of  electrolytes  alone.  For  example, 
the  percentage  equivalent  solubility  depression  of  hydrogen  in  water  in 
the  presence  of  sugar  at  normal  concentration  is  32.  Similarly,  the 
equivalent  depression  of  hydrogen  at  the  same  concentration  at  20°  is 
9.2  for  chloral  hydrate.  The  depression  for  sugar  is  greater  than  that  for 
most  salts,  while  that  for  chloral  hydrate  is  greater  than  that  for  the 

"Euler,  Ztschr.  f.  pliys.  CJiem.  1$,  310  (1904). 


HETEROGENEOUS  EQUILIBRIA 


249 


§      I 

8'*OOO t>»O5 
§        •      -      '-"H <M<N 

jz  *S? 

PQ 

&  I       '     '     '     ' 

H  ^ 

gs    :<°S;3  :  :2  :  :35S  :  :  :  :  :     : 
S 

|      Sa  |     '  I     "j        'I 

I     111  *]•  :  :°°2  :S8  :888  :£38  :  || 

§  ^c3          0  ^  o  <N  ^      ^ 

2g          ^"3        •  <^      -CO      •  CO  ^      .      .  T}<      .      .      .      .  10  *O  »O     ^ 

HH        t>    J 

!«  j 

H   H         rr,  *?  ^  ^  «3 

[IX  rt^  «  rHCSlOO5rH*Tfl'*»OOO  (Nl^-  52 

PQ  ^g  H  rH-rH'-rHrH''<M<N'^g 

aS  O  CO**OiOt>-*'*rH«OOt<N**Ofl 

Q  g  •       •  rH  rH       •       •       •  W       'COCO       'CO       •       •      «2  JU 

|  .        .    .   .    .    .    .   .„   .s gS 

o  TtlCOiOOiCO  OQ  _O 

O      |2     •   '   "   • 
<J 

W*   I   !   "   *  CO  O   *  rH  rH   \  CO  CO   ]  !>•  O5   ".   " 
rH  (N    C^l  <N    <M  <N    <M  -M 

H  ...„.,.,,.- 


O 

^ 
W^rt 


250        PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

acids.  Obviously,  the  "salting  out"  effect  cannot  well  be  ascribed  to 
some  property  peculiar  to  electrolytes  alone. 

In  a  few  instances,  the  addition  of  a  salt  causes  a  marked  increase 
in  the  solubility  of  a  non-electrolyte.  This  is  the  case  with  ether  in 
water  in  the  presence  of  sodium  salts  of  aromatic  acids.18  While  the 
salts  of  the  aliphatic  acids  cause  a  marked  depression  in  the  solubility, 
those  of  the  aromatic,  acids  cause  an  increase  in  solubility. 

In  Table  XCVIII  are  given  values  of  the  equivalent  percentage  solu- 
bility increase  of  ether  in  water  due  to  the  addition  of  0.5  N  salts  of 
different  acids. 

TABLE   XCVIII. 

SOLUBILITY  CONSTANTS  FOR  ETHER  IN  THE  PRESENCE  OF  SODIUM  SALTS 

OF  AROMATIC  ACIDS. 

Solubility 
Salt  Solubility          Coefficient 

0.5  N  Sodium  Phthalate    ...............  5.88  1.5 

0.5  N  Sodium  Cinnamate    ..............  6.29  15.0 

0.5  N  Sodium  Benzoate  ................  5.99  4.8 

0.5  N  Sodium  Salicylate    ...............  6.44  20.0 

0.5  N  Sodium  Benzenesulphonate    .......  6.05  7.0 

The  solubility  of  ether  is  given  in  the  second  column.  The  solu- 
bility of  ether  in  pure  water  is  5.85  grams  per  100  grams  of  water  at  28°. 
It  is  evident  that  the  so-called  "salting  out"  effect  is  not  a  property 
characteristic  of  all  electrolytes. 

It  is  of  interest  to  examine  the  solubility  effects  in  non-aqueous  solu- 
tions. Here  the  data  are  very  meager.  Thorin19  has  measured  the 
solubility  of  phenylthiourea  in  ethyl  alcohol  at  28°.  The  results  are 

TABLE   XCIX. 

SOLUBILITY  OF  PHENYLTHIOUREA  IN  ETHYL  ALCOHOL  IN  THE  PRESENCE 

OF  ELECTROLYTES. 

Electrolyte  Concentration  Solubility  B' 

LiCl  ..............  0.168  norm.  0.2274  norm.  60 

"  ..............  0.337  0.2360  42 

"  ..............  0.673  0.2440  27 

"  ..............  1.346  0.2494  15 


18  Thorin,  Ztschr.  f.  phys. 
"Ibid.,  89,  691    (1915). 


Chem.  89,  688  (1915). 


HETEROGENEOUS  EQUILIBRIA  251 

TABLE  XCIX.— Continued 

Electrolyte  Concentration  Solubility  B' 

CaCl2 0.061  0.2101  28 

"      0.122  0.2135  28 

"       0.244  0.2194  25 

"      0.487  0.2279  21 

"      0.975  0.2372  15 

NaJ  0.043  0.2102  42 

"  0.086  0.2148  46 

"  0.172  0.2198  37 

"  0.343  0.2271  29 

"  0.685  0.2359  21 

NaBr  0.022  0.2098  73 

"       0.043  0.2194  66 

"      0.086  0.2165  57 

0.172  0.2257  54 

given  in  Table  XCIX.  The  solubility  in  pure  alcohol  is  0.2065  grams 
per  hundred  grams  of  solvent.  The  equivalent  percentage  solubility  in- 
crease is  given  in  the  last  column  under  B'. 

It  will  be  observed  that  the  solubility  coefficient  is  initially  quite 
large  and  decreases  markedly  at  the  higher  concentrations.  The  solu- 
bility is  in  all  cases  increased,  but,  as  in  the  case  of  aqueous  solution,  the 
solubility  effect  is  a  property  of  the  electrolyte  in  question.  The  effect 
is  greatest  for  lithium  chloride,  in  which  case  the  solubility  is  increased 
approximately  20  per  cent  in  a  normal  solution  of  the  electrolyte. 

Some  writers  have  ascribed  the  depression  of  the  solubility  of  non- 
electrolytes  in  water,  due  to  electrolytes,  to  the  action  of  the  ions 
upon  the  non-electrolyte.  If  any  interaction  of  this  kind  actually  takes 
place,  it  must  be  of  a  secondary  nature,  and  greatly  qualified  by  the 
nature  of  the  ions  with  which  the  charges  are  associated.  The  increase 
in  the  solubility  of  phenylthiourea  in  alcohol  clearly  indicates  that  the 
action  of  the  salt  upon  the  non-electrolyte  is  greatly  affected  by  the 
nature  of  the  solvent  medium.  Further  experimental  data  on  the  effects 
of  salts  on  the  solubility  of  non-electrolytes  in  non-aqueous  solutions  are 
of  much  interest. 

4.  Solubility  of  Salts  in  the  Presence  of  Non-Electrolytes.  The 
solubility  of  salts  in  aqueous  solutions  is  in  general  depressed  by  the 
addition  of  non-electrolytes.  The  solubility  change,  as  a  rule,  follows 
very  nearly,  although  not  quite,  a  linear  relation.  In  the  following  table 
are  given  values  for  the  solubility  of  lithium  carbonate  in  water  at  25°  in 


252        PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

the  presence  of  various  non-electrolytes,  at  different  concentrations.20 
The  solubility  of  lithium  carbonate  in  pure  water  is  0.1687  equivalents 
per  liter. 

TABLE  C. 

SOLUBILITY  OF  LITHIUM  CARBONATE  IN  THE  PRESENCE  OF 
NON-ELECTROLYTES. 

Mols  of  non-electrolyte  %-  %-  %-        1-norm. 

1.  Methyl  alcohol 0.1604  0.1529  0.1394 

2.  Ethyl  alcohol 0.1614  0.1555  0.1417  0.1203 

3.  Propyl  alcohol  0.1604     •   0.1524  0.1380  0.1097 

4.  Amyl  alcohol  (tertiary)   . .  0.1564  0.1442  0.1224  0.0899 

5.  Acetone  0.1600  0.1515  0.1366  0.1104 

6.  Ether  0.1580  0.1476  0.1300          

7.  Formaldehyde    0.1668  0.1653  0.1606  0.1531 

8.  Glycol    0.1660  0.1629  0.1565  0.1472 

9.  Glycerine   0.1670  0.1647  0.1613  0.1532 

10.  Mannite   0.1705  0.1737  0.1778 

11.  Grape  sugar 0.1702  0.1728  0.1752  0.1778 

12.  Cane  sugar    0.1693  0.1689  0.1661  0.1557 

13.  Urea    0.1686  0.1673  0.1643  0.1605 

14.  Thiourea   0.1667  0.1643  0.1600  0.1523 

15.  Dimethylpyrone 0.1562  0.1460  0.1284  0.0992 

16.  Ammonia   : 0.1653  0.1630  0.1577  0.1466 

17.  Diethylamine   0.1589  0.1481  0.1283  0.0937 

18.  Pyridine  0.1592  0.1503  0.1347  0.1091 

19.  Piperidine 0.1584  0.1488  0.1320  0.1009 

20.  Urethane  0.1604  0.1525  0.1377  0.1113 

21.  Acetamide    0.1614  0.1520  0.1358 

22.  Acetonitrile    0.1618  0.1556  0.1429  0.1178 

23.  Mercuric  cyanide 0.1697  0.1704          

It  will  be  observed  that,  with  a  few  exceptions,  of  which  mannite  and 
grape  sugar  are  the  most  striking  examples,  the  solubility  is  depressed  by 
the  addition  of  non-electrolytes.  In  general,  the  depression  is  the  greater 
the  smaller  the  dielectric  constant  of  the  added  non-electrolyte,  although 
this  relation  does  not  hold  exactly,  since,  for  example,  the  addition  of 
ether  causes  a  smaller  decrease  in  the  solubility  than  does  that  of  amyl 
alcohol.  With  increasing  complexity  of  the  carbon  group  the  depression 
of  the  solubility,  in  general,  increases.  The  solubilities  may  be  expressed 
approximately  as  a  function  of  concentration  by  Equation  63. 

In  the  following  table  are  given  the  values  of  100 13  for  solutions  of  a 
number  of  salts  in  water  in  the  presence  of  non-electrolytes.21    The  non- 
80  Rothmund,  Ztschr.  J.  phya.  Chem.  69.  531  (1909). 
«  Rothmund,  loc.  cit. 


HETEROGENEOUS  EQUILIBRIA  253 

TABLE    CI. 

SOLUBILITY  OF  LiC03,  Ag2S04,  KBr03,  KC104,  Sr(OH)2.8H20  AT  25°  IN 
THE  PRESENCE  OF  ELECTROLYTES. 

Values  of  100  p. 

Li2C03        Ag2SO4  KBrO3  KC1O*  Sr(OH)2.8H,0 

Amyl   alcohol    (tert.) . .     63.0          54.2  44.3  28.5          54.1 

Dimethyipyrone    56.1             ..  43.8  19.3          71.0 

Ether  52.4          52.2  38.1  19.8          51.3 

Dimethylpyrone 54.6          42.7 

Piperidine 50.5            ..  37.6 

Formaldehyde    (9.5)        32.4  37.1 

Methylal 53.1  33.1  10.5 

Propyl  alcohol 41.7          40.4  31.2  18.7          32.6 

Pyridine 44.4            ..  28.3  9.0          36.7 

Methylacetate 46.5  25.9  6.4 

Acetonitrile    34.6  (—  134.8) 

Ethyl  alcohol   33.6          31.9  24.9  10.8          22.8 

Chloral 27.9 

Acetone   42.4          39.1  23.5  3.3          37.5 

Phenol (—70.0)  23.0  16.0 

Cane  sugar  (5-0)     (— 1.5)  20.7 

Urethane  41.0          36.7  18.7  10.5 

Methyl  alcohol 19.3          22.1  14.7  10.1            3.4 

Acetamide   20.8          10.7  14.4  3.8 

Ammonia  14.0            ..  14.3  0.1          12.3 

Glycol   14.2          10.3  10.3  8.2    (—19.9) 

Thiourea  10.3 

Glycerine  ............       9.3            3.4  11.6  9.8    (—54.3) 

Mannite   (-10.5)  (—  20.3)  11.6  . .      (— 174) 

Acetic  acid 12.3  9.4  1.5 

Grape  sugar (—6.6)  (— 11.6)  6.3 

Formamide (—2.2)  1.1  —8.5 

Urea    4.5    (—25.3)  0.0  —4.7            3.6 

Glycocoll    ..     (—96.3)  —9.4 

electrolytes  are  arranged  vertically  in  the  order  of  their  effect  on  the 
solubility  of  potassium  bromate.  Those  values  which  appear  in  paren- 
theses in  the  table  are  such  in  which  interaction  between  the  non-electro- 
lyte and  the  electrolyte  probably  occurs.  A  negative  value  of  the  solu- 
bility coefficient  indicates  an  increase  in  the  solubility.  With  the  possible 
exception  of  potassium  bromate  in  the  presence  of  glycocoll  and  potas- 
sium perchlorate  in  the  presence  of  formamide  and  urea,  the  increased 
solubilities  are  probably  to  be  ascribed  to  interaction  between  the  elec- 
trolyte and  the  non-electrolyte. 


254        PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

For  lithium  carbonate,  silver  sulphate,  potassium  bromate,  and  potas- 
sium perchlorate,  there  is  a  rough  parallelism  in  the  order  of  the  solu- 
bility effects  among  the  different  electrolytes  in  the  presence  of  a  non- 
electrolyte,  although  numerous  exceptions  occur,  particularly  in  the  case 
of  lithium  carbonate.  So,  also,  the  solubility  effect  in  general  decreases 
in  the  order  lithium  carbonate,  silver  sulphate,  potassium  bromate,  potas- 
sium perchlorate,  although  here,  again,  exceptions  are  found.  There  can 
be  no  question,  however,  that  a  parallelism  exists  between  the  solubility 
effects  for  different  salts  and  for  different  electrolytes.  Roughly,  those 
non-electrolytes  which  suffer  the  greatest  solubility  change  on  the  addi- 
tion of  a  non-electrolyte  cause  the  greatest  change  in  the  solubility  of  a 
given  electrolyte,  and  those  electrolytes  which  cause  the  greatest  change 
in  the  solubility  of  a  given  non-electrolyte  suffer  the  greatest  solubility 
change  on  the  addition  of  a  given  non-electrolyte.  These  relations,  how- 
ever, are  only  roughly  true.  It  is  again  evident  that  the  effect  of  different 
non-electrolytes  on  the  solubility  of  electrolytes  is  primarily  a  function 
of  the  nature  of  the  electrolyte  and  of  the  added  non-electrolyte.  Similar 
measurements  on  the  solubility  effects  in  non-aqueous  solvents  do  not 
exist. 

5.  Solubility  of  Electrolytes  in  the  Presence  of  Other  Electrolytes. 
If  an  electrolyte  is  added  to  a  solution  of  another  electrolyte,  which  is 
present  as  a  solid  phase  in  equilibrium  with  its  solution,  the  solubility 
effect  will  obviously  depend  upon  the  interaction  between  the  two  elec- 
trolytes. Since  electrolytes  in  solution  are  ionized  and  equilibrium  estab- 
lishes itself  almost  instantaneously,  it  is  to  be  expected  that  various 
effects  will  be  observed.  We  have  to  consider  here  two  cases  which  are 
of  practical  importance :  First,  the  solubility  of  an  electrolyte  in  the  pres- 
ence of  another  electrolyte  with  a  common  ion;  and,  second,  the  solubility 
of  an  electrolyte  in  the  presence  of  another  electrolyte  without  a  com- 
mon ion. 

a.  Solubility  of  Weak  Electrolytes  in  the  Presence  of  Strong  Electro- 
lytes with  an  Ion  in  Common.  If  the  law  of  mass-action  is  applicable, 
the  addition  of  a  binary  electrolyte  to  a  second  binary  electrolyte  having 
an  ion  in  common  should  cause  a  depression  in  the  solubility  of  the  second 
electrolyte.  We  have  the  equations: 

M:  x  x,- 

~~ 


HETEROGENEOUS  EQUILIBRIA  255 

it  being  assumed  that  the  two  electrolytes  have  a  negatives  ion  X~  in 
common.  Here,  Su  is  the  concentration  of  the  un-ionized  fraction  of  the 

first  electrolyte,  which  is  assumed  to  be  present  in  excess,  so  that  there 
exists  an  equilibrium  between  the  solid  salt  M1X1  and  the  solution.  If 
the  laws  of  ideal  solutions  hold,  the  concentration  Su  of  the  un-ionized 

fraction  of  the  first  salt  should  remain  constant.  The  total  concentra- 
tion S  of  the  first  salt  is  then  given  by  the  equation: 

(65)  S  =  M+  +  SU. 

If  a  second  electrolyte  with  a  common  ion  X1  is  added,  then,  in  the  mix- 
ture, we  have  the  equilibrium  expressed  by  the  equation: 

M 

(66) 


o  —     i, 

Su 

where  M^  +  M2+  is  the  concentration  of  the  common  ion  X~,  which  we 
may  write  2C.    It  follows  from  Equation  66  that: 


(67) 


and  substituting  for  this  value  in  Equation  65,  we  have  for  the  solubility 
the  expression: 

K^SU 

(68)  s  =  S+-, 


An  examination  of  this  equation  shows  that  the  addition  of  an  electrolyte 
with  a  common  ion  reduces  the  solubility  of  the  first  electrolyte.  If  we 
plot  values  of  S  as  ordinates  and  those  of  2C^  as  abscissas,  the  resulting 

curve  will  be  a  rectangular  hyperbola,  whose  axis  is  raised  above  the 
origin  by  the  distance  S  .  As  the  concentration  of  the  added  electrolyte, 

and  consequently  the  concentration  of  the  common  ion,  is  increased 
indefinitely,  the  solubility  approaches  the  value  Su  as  a  limit.  The  rep- 

resentation of  solubility  results  is  greatly  simplified  if  the  solubility  is 
plotted  against  the  reciprocal  of  the  common  ion  concentration,  ia  which 
case  a  linear  curve  obviously  results.  This  curve  ends  in  a  point 


256        PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

where  /S0  is  the  solubility  of  the  first  electrolyte  in  pure  water  and  M01+ 
is  the  ion  concentration  in  this  solution.  As  the  reciprocal  of  the  total 
ion  concentration,  1/2C-,  or  the  common  ion  dilution  2F^,  decreases,  the 

solubility  decreases  as  a  linear  function1  of  this  variable,  approaching  the 
value  S  =  & .  at  1/2C .  =  0. 

U>  (/ 

If  S,    is  a  constant,  as  it  is  if  the  laws  of  ideal  solutions  hold,  and  if 

tv 

K!  is  a  constant,  then  it  follows  from  Equation  66  that 
(69)  Ml*XX-  =  K1Su  =  K, 

where  X~  is  the  concentration  of  the  common  ion  in  the  solution,  and  K 
is  a  constant.  For  an  electrolyte  in  solution  in  equilibrium  with  its 
solid  phase,  the  product  of  the  concentrations  of  the  ions  remains  con- 
stant, provided  that  the  laws  of  dilute  solutions  hold.  According  to  these 
considerations,  the  solubility  of  a  given  electrolyte  may  be  depressed  to  a 
value  which  corresponds  to  the  concentration  of  the  un-ionized  fraction 
in  a  solution  of  the  pure  electrolyte  in  equilibrium  with  its  solid  phase. 

The  foregoing  relations  are  based  on  the  assumption  that  the  laws 
of  dilute  solutions  are  applicable.  As  we  have  seen,  this  condition  is  not 
fulfilled  in  solutions  of  strong  electrolytes.  The  effect  of  the  presence 
of  strong  electrolytes  upon  the  solubility  of  other  strong  or  weak  elec- 
trolytes can,  therefore,  be  determined 'by  experiment  only.2**  The  con- 
centration of  the  various  molecular  species  in  the  mixture  cannot  be  deter- 
mined, even  though  the  solubility  of  the  first  electrolyte  is  known,  unless 
a  law  is  assumed  governing  the  equilibrium  of  the  various  electrolytes 
present  in  the  mixture;  and  the  results  obtained  for  the  concentration  of 
the  ionized  and  the  un-ionized  fraction  of  the  first  salt  in  the  mixture, 
as  calculated,  will  depend  upon  the  laws  assumed  as  governing  the  equi- 
librium in  the  mixture. 

We  shall  first  examine  the  effect  of  strong  and  weak  electrolytes  upon 
the  solubility  of  weak  electrolytes;  that  is,  electrolytes  which  conform 
to  the  simple  mass-action  law.  Such  determinations  have  been  made  by 
Kendall.22 

In  Table  CII  is  given  values  for  the  solubility  of  a  number  of  weak 
acids  in  the  presence  of  other  acids,  both  weak  and  strong. 

The  results  are  shown  graphically  in  Figures  49  and  50.  Considering 
first  the  .solubility  of  orthonitrobenzoic  acid  and  salicylic  acid  in  th< 

m  It  is  evident  from  Equation  69  that  KI  and  8U  might  vary  in  such  a  manner  tha 

their  product  would  remain  constant,  in  which  case  the  ion  product  would  remain  con 
stant.     It  is  very  improbable,  however,  that  such  a  compensation  actually  occurs. 
"Kendall,  Proc,  Roy.  Soc.  85 A,  218  (1911). 


HETEROGENEOUS  EQUILIBRIA  257 

TABLE  GIL 
SOLUBILITY  OP  WEAK  ACIDS  IN  THE  PRESENCE  OF  OTHER  ACIDS. 

A.    Salicylic  Acid  in  the  Presence  of  Formic  Acid. 

Solubility,  Solubility, 

Formic  acid,  gravimetric,  volumetric, 

per  cent.  mols  per  liter.  mols  per  liter. 

0.00  0.01631  0.01634 

0.24  0.01531 

0.46  ....  0.01474 

0.625  0.01484 

1.25  0.01496 

2.5  0.01536 

5.0  0.01716  

10.0  0.02101 

B.    Solubility  of  Hippuric  Acid  in  the  Presence  of  Formic  Acid. 

Solubility,  Solubility, 

Formic  acid,  gravimetric,  volumetric, 

per  cent.  mols  per  liter.  mols  per  liter. 

0.00  0.02045  0.02048 

1.25  0.02014 

2.5  0.02078 

5.0  0.02275 

10.0  0.02661  

C.    Solubility  of  Salicylic  Acid  in  the  Presence  of  Acetic  Acid. 

Acetic  acid,  Solubility,  gravimetric, 

per  cent.  mols  per  liter. 

£  0.00  0.01631 

0.625  0.01691 

1.25  0.01745 

2.5  0.01846 

5.0  0.02059 

D.    Solubility  of  Salicylic  Acid  in  the  Presence  of  Hydrochloric  Acid. 

Hydrochloric  Solubility,  Solubility, 

acid,  gravimetric,  volumetric, 

normal.  mols  per  liter.  mols  per  liter. 

0.01631  0.01634 

0.0179  0.01290 

0.0357  ....  0.01238 

0.125  0.01214 

0.25  0.01194 

0.5  0.01123 


258       PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 


TABLE  GIL— Continued 

E.    Solubility  of  o-Nitrobenzoic  Acid  in  the  Presence  of 
Hydrochloric  Acid. 

Hydrchloric  Solubility,  Solubility, 

acid,  gravimetric,  volumetric, 

normal.  mols  per  liter.  mols  per  liter. 

0.04320  0.04360 

0.0179  0.03681 

0.0357  ....  0.03390 

0.125  0.02980 

0.25  0.02922 

0.5  0.02846 

presence  of  hydrochloric  acid,  it  will  be  observed  that  the  solubility  de- 
creases greatly  on  the  initial  addition  of  hydrochloric  acid,  after  which 
the  solubility  decreases  slightly,  practically  as  a  linear  function  of  the 
concentration.  In  the  presence  of  the  weaker  acids,  the  initial  decrease 


O.04 


O.OJ 


0.01 


O-NlTROBENZOC  AoO  IN  HCt 


SALICYLIC  ACID  IN  HG. 


0.0 


6.S 


O.I  0.2  O.3 

Concentration  of  Added  Acid. 

FIG.  49.    Solubility  of  Moderately  Strong  Organic  Acids  in  Water  in  the  Presence 
of  Hydrochloric  Acid   at  25°. 

is  relatively  slight,  and  this  decrease  is  the  smaller  the  weaker  the  added 
acid.  The  solubility  of  salicylic  acid  in  the  presence  of  acetic  acid 
increases  from  the  beginning.  In  the  case  of  the  organic  acids  the  solu- 
bility eventually  increases,  practically  as  a  linear  function  of  the  con- 
centration of  the  added  acid.  The  results  are  in  harmony  with  the 


HETEROGENEOUS  EQUILIBRIA 


259 


assumption  that  the  initial  depression  in  the  solubility  of  the  acid  is  due 
to  the  depression  of  its  ionization.  Acetic  acid  is  so  weak  that,  even  at 
fairly  high  concentrations,  it  has  no  appreciable  effect  on  the  ionization 
of  salicylic  acid,  and  consequently  the  resulting  curve  merely  measures 
the  increase  in  the  solubility  of  the  un-ionized  fraction.  In  the  case  of 
hippuric  and  salicylic  acids  in  formic  acid,  the  added  acid  is  sufficiently 
strong  to  practically  completely  repress  the  ionization  of  salicylic  acid 
present  in  solution.  In  these  cases,  therefore,  there  is  an  initial  decrease 
in  the  solubility,  while  finally,  when  the  ionization  is  completely  repressed, 
the  solubility  is  increased,  owing,  presumably,  to  the  increased  solubility 
of  the  un-ionized  molecules  of  the  first  acid  on  addition  of  the  second. 
By  extrapolating  the  linear  solubility  curves  backwards,  until  they  inter- 

Per  Cent  of  Added  Acid. 
O       I        e       y      4        s       6       7       s       9      to 


o.ois 


02 


O.Olf 


FIG.  50.    Solubility  of  Weak  Organic  Acids  in  Water  in  the  Presence   of  Other 

Organic  Acids  at  25°. 

sect  the  axis  of  solubility,  the  intercepts  on  this  axis  correspond  approxi- 
mately to  the  solubility  of  the  un-ionized  fraction  in  pure  water. 

It  will  be  noted  that  the  solubility  of  salicylic  acid  and  of  orthonitro- 
benzoic  acid  is  depressed  according  to  the  requirements  of  the  mass-action 
law  not  only  on  addition  of  weak  acids,  but  also  on  addition  of  hydro- 
chloric acid.  In  this  case,  the  solubility  of  the  un-ionized  fraction  in  the 
more  concentrated  solutions  decreases  slightly  with  increasing  concen- 
tration of  hydrochloric  acid.  The  initial  depression  effect  is  marked, 
particularly  in  the  case  of  orthonitrobenzoic  acid,  which  is  a  fairly  soluble 
acid.  Apparently,  the  addition  of  a  strong  acid  to  a  solution  of  a  weak 
acid,  as  well  as  the  addition  of  a  weak  acid  to  a  solution  of  a  weak  acid, 
does  not  greatly  alter  the  ionization  constant  of  weak  acids.  The  ioniza- 
tion constant  of  salicylic  acid  at  25°  is  1.02  X  10~3;  that  of  hippuric  acid 
is  2.22  X  10-4;  and  orthonitrobenzoic  acid  6.16  X  10"3. 


260       PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

Kendall  and  Andrews  22a  have  recently  extended  the  investigation  of 
the  solubility  of  acids  in  the  presence  of  weak  acids.  They  have  meas- 
ured the  solubility  of  acids  of  varying  strength  and  solubility  in  the 
presence  of  both  strong  and  weak  acids  up  to  high  concentrations.  They 
include  hydrogen  sulphide,  carbonic  acid,  boric,  oxalic,  succinic,  trichloro- 
acetic,  m-nitrobenzoic,  3-5-dinitrobenzoic,  benzoic,  picric  and  (3-naph- 
thalene  sulphonic  acids  in  the  presence  of  hydrochloric  acid ;  and  suberic, 
mandelic,  succinic,  oxalic,  tartaric  and  boric  acids  in  the  presence  of 
acetic  acids  up  to  concentrations  of  10  normal  added  acid.  They  have 
also  measured  the  solubility  of  boric,  benzoic  and  salicylic  acids  in  the 
presence  of  nitric  acid. 

The  solubility  of  all  acids  on  addition  of  a  strong  acid  is  initially 
decreased.  On  addition  of  larger  amounts  of  the  strong  acid  the  solu- 
bility, with  a  few  exceptions,  passes  through  a  minimum.  At  high  con- 
centrations of  the  added  acid,  the  solubility  increase  is  very  marked  in 
some  cases  while,  in  a  few,  the  minimum  is  lacking.  The  initial  decrease 
appears  to  be  due  to  a  repression  of  the  ionization  of  the  saturating  acid. 
The  stronger  the  acid,  the  greater  is  the  initial  depression,  while  in  the 
case  of  very  weak  acids  the  initial  depression  is  wanting.  The  minimum 
solubility  of  an  acid  is  much  lower  than  corresponds  to  the  concentration 
of  its  un-ionized  molecules  in  pure  water.  This  is  ascribed  to  the  depres- 
sion of  the  solubility  because  of  hydration  effects  accompanying  the  addi- 
tion of  the  strong  acid.  It  may  be  noted  that  the  maximum  depression 
of  hydrogen  sulphide  and  carbonic  acids  is  very  low,  amounting  to  only 
a  few  per  cent.  The  final  rise  in  the  solubility  curve  is  ascribed  to  the 
formation  of  compounds  between  the  two  acids  at  high  concentrations. 
This  view  is  supported  by  the  results  of  conductance  measurements  which 
indicate  the  formation  of  complexes.  This  accounts  for  the  widely 
divergent  effect  of  strong  acids  on  different  weak  acids  at  higher  concen- 
trations. The  solubility  curves  for  weak  acids  in  the  presence  of  acetic 
acid  exhibit  a  great  variety  of  form.  Here,  the  common  ion  effects  at 
low  concentration  of  added  acid  are  approximately  as  might  be  expected. 

The  effect  of  strong  and  weak  acids  on  the  un-ionized  fraction  of  weak 
acids  does  not  differ  greatly  from  that  observed  in  the  case  of  non-elec- 
trolytes. For  example,  the  solubility  of  hydrogen  in  water  is  only  very 
slightly  depressed  due  to  the  addition  of  acetic  acid,  but  somewhat  more 
strongly  due  to  the  addition  of  hydrochloric  acid.  In  a  normal  solution 
of  hydrochloric  acid,  the  solubility  depression  in  the  case  of  hydrogen  is 
7  per  cent  and  that  in  the  case  of  the  undissociated  fraction  of  orthonitro- 
benzoic  acid  10  per  cent.  The  percentage  depression  in  the  case  of  sali- 

"•  Kendall  an<J  Andrews,  /.  Am.  Chem.  Soc.  $3,  1545  (1921). 


HETEROGENEOUS  EQUILIBRIA  261 

cylic  acid  is  considerably  greater.  It  appears,  therefore,  that,  on  the 
addition  of  an  electrolyte,  so  far  as  the  solubility  relations  are  concerned, 
substances  with  polar  molecules  are  affected  in  the  same  way  as  are  those 
with  non-polar  molecules.  With  polar  substances,  the  same  specific 
effects  are  found  which  are  characteristic  of  non-polar  substances.  At 
high  concentrations  of  the  added  acid,  the  specific  nature  of  the  effects 
indicates  some  manner  of  interaction  between  the  two  acids. 

b.  The  Solubility  of  Strong  Binary  Electrolytes  in  the  Presence  of 
Other  Strong  Electrolytes.  The  solubility  of  a  strong  electrolyte  is,  in 
general,  depressed  on  the  addition  of  another  strong  electrolyte  having  a 
common  ion.  On  the  addition  of  a  salt  without  a  common  ion,  the 
solubility  is  in  general  increased,  presumably  owing  to  the  formation  of 
un-ionized  molecules  as  a  consequence  of  a  metathetic  reaction.  The 
relations  are  much  simpler  with  binary  electrolytes  than  with  electrolytes 
of  higher  type.  The  solubility  relations  are  also  greatly  affected  by  the 
concentration  of  the  electrolyte,  whose  solubility  is  under  consideration. 

In  Table  CIII  are  given  values  for  the  solubility  of  thallous  chloride 
in  water  at  25°  in  the  presence  of  various  electrolytes.23  The  results  are 

TABLE  CIII. 

SOLUBILITY  OF  THALLOUS  CHLORIDE  IN  THE  PRESENCE  OP  OTHER 

ELECTROLYTES. 

Cone,  of 
added  salt  HC1       KC1      BaCl2   T1N03    T12S04   KNOa 


10  

....    16.07 

16.07 

16.07 

16.07 

1607 

1607 

1607 

20  

1034 

17  16 

17  79 

25  

8.66 

8.69 

8.98 

8.80 

50  

....       583 

590 

618 

624 

677 

1826 

1942 

100  

3.83 

3.96 

4.16 

422 

468 

1961 

21  37 

200  

2.53 

2.68 

2.82 

300  , 

23  13 

2600 

1000  . 

30.72 

34.1fi 

shown  graphically  in  Figure  51.  An  examination  of  the  table  and  the 
figure  shows  that  the  solubility  change  in  the  case  of  different  electro- 
lytes is  of  the  same  order  of  magnitude  for  salts  of  the  same  type.  The 
depression  due  to  the  addition  of  hydrochloric  acid  is  slightly  greater 
than  that  due  to  potassium  chloride  or  thallous  nitrate.  Ternary  salts, 
having  an  ion  in  common  with  thallous  chloride,  cause  a  depression  which 
is  very  nearly  the  same  as  that  of  binary  salts.  The  solubility  is 
markedly  increased  due  to  the  addition  of  salts  without  a  common  ion. 
While  the  solubilities  due  to  the  addition  of  different  salts  differ,  this 

"Bray  and  Winninghoff,  J.  Am.  Chem.  8oc.  S3,  1671  (1911). 


262        PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 


difference  is  in  general  much  smaller  than  in  the  case  of  solutions  of  non- 
electrolytes. 

It  is  not  possible  to  determine  the  concentration  of  the  un-ionized 
fraction  in  mixtures  of  electrolytes  without  assuming  a  law  governing 

0-014 


«    0.0*0 

^ 


U 


o.on 


TICI 


o.oo        o.oz         00+        o.oe        0.O8        0,10        o./z         a. /-f-         o./f 
Concentration  of  Added  Salt  in  Equivalents  per  Liter. 

FIG.  51.    Solubility  of  Thallous  Chloride  in  Water  in  the  Presence  of  Other 

Electrolytes. 

the  ionization  of  electrolytes  in  mixtures.  As  a  rule,  the  iso-ionic  prin- 
ciple has  been  employed  for  this  purpose.  In  Table  CIV  are  given  values 
for  the  concentration  of  the  un-ionized  fraction,  T1C1,  and  the  ion  product, 
Tl+  X  Cl~,  for  solutions  of  thallous  chloride  in  the  presence  of  different 
electrolytes  at  25°  24,  the  isohydric  principle  being  assumed  to  hold  for 

the  mixtures. 

TABLE    CIV. 

CALCULATED  VALUES  OF  THE  ION  PRODUCT  AND  THE  CONCENTRATION  OF 

THE  UN-IONIZED  FRACTION  FOR  THALLOUS  CHLORIDE  IN  WATER 

AT  25°  IN  THE  PRESENCE  OF  DIFFERENT  ELECTROLYTES. 


Cone.  0          20        25 

(T1C1 1.755  1.338 

JTl+XCl-   ....  204.9  211.0 

JT1C1 1.755  1.465 

(T1+XC1-   ....  204.9  208.1 

JT1C1 1.755  1.343 

(T1+XC1-   ....  204.9  217.4 

Cone.  0          20        25 

JT1C1  1.755        ..       1.390 

(T1+XC1-  ....  204.9        ..       218.1 

2*  Bray  and  Winninghoff,  loc.  cit. 


Added  Salt 
1/2  K2S04 

1/2T12S04 
KN03 

KC1 


50 
1.120 
218.3 
1.239 
215.7 
1.124 
229.1 
50 
1.204 
229.6 

100 
0.966 
229.7 
1.087 
231.3 
0.968 
243.0 
100 
1.061 
256.3 

300 
0.768 
258.6 

0.775 
279.2 
200 
0.94 
290.0 

HETEROGENEOUS  EQUILIBRIA  263 

It  will  be  observed  that,  according  to  these  calculations,  the  concen- 
tration of  the  un-ionized  fraction  decreases  markedly  as  the  concentra- 
tion of  the  added  electrolyte  increases.  In  a  0.3  normal  solution  of 
potassium  sulphate,  the  calculated  concentration  is  less  than  one  half 
that  in  pure  water.  The  ion  product  increases  due  to  the  addition  of 
the  second  electrolyte,  this  increase  depending  upon  the  nature  of  the 
added  electrolyte.  On  the  addition  of  0.3  N  equivalents  of  potassium 
sulphate,  the  ion  product  increases  from  204.9  to  258.6.  .  On  the  addition 
of  0.2  N  equivalents  of  potassium  chloride,  the  ion  product  increases  from 
204.9  to  290.0.  The  increase  in  the  case  of  potassium  chloride,  there- 
fore, is  approximately  twice  that  for  potassium  sulphate.  If  the  assump- 
tions underlying  these  calculations  are  correct,  the  concentration  of  the 
un-ionized  fraction  is  greatly  reduced  on  the  addition  of  a  relatively  small 
amount  of  a  second  electrolyte.  Since  it  has  commonly  been  assumed 
that  the  isohydric  principle  holds  for  strong  electrolytes,  many  writers 
have  accepted  as  correct  the  result  that  the  concentration  of  the  un- 
ionized fraction  of  the  salt  is  greatly  depressed  on  the  addition  of  an 
electrolyte.  As  was  pointed  out  in  a  preceding  section,  the  applicability 
of  the  iso-ionic  principle  to  mixtures  of  strong  electrolytes  is  doubtful. 
It  is  doubtful,  therefore,  that  the  above  values  represent  correctly  the 
state  of  the  solutions  in  question. 

The  solubility  depression  of  the  un-ionized  fraction  is  much  greater 
than  might  be  expected  from  the  effect  of  electrolytes  upon  the  solubility 
of  non-electrolytes.  The  solubility  depression  of  hydrogen  in  water  at 
15°  for  different  salts  at  normal  concentration  is  in  the  neighborhood  of 
20  per  cent,  that  of  oxygen  in  the  neighborhood  of  30  per  cent,  and  that 
of  nitrous  oxide  in  the  neighborhood  of  20  per  cent.  The  solubility  de- 
pression of  phenylthiourea  at  normal  concentration  of  the  added  salt  is 
24  per  cent  for  potassium  chloride,  10  per  cent  for  sodium  nitrate,  and 
for  ammonium  nitrate  there  is  a  solubility  increase  of  7  per  cent.  The 
solubility  curves,  moreover,  while  not  quite  linear,  are  only  slightly 
convex  toward  the  axis  of  concentrations.  Furthermore,  on  the  addition 
of  hydrochloric  acid,  the  solubility  depression  of  non-electrolytes  is  rela- 
tively very  small.  At  normal  concentration  and  25°,  it  is  7  per  cent  for 
hydrogen,  6.8  per  cent  for  oxygen,  and  4.4  per  cent  for  nitrous  oxide. 
From  the  effect  of  electrolytes  on  the  solubility  of  non-electrolytes,  it 
must  be  concluded,  not  only  that  the  effect  varies  greatly  with  the  nature 
of  the  added  electrolyte,  but,  also,  that  the  magnitude  of  the  effect  is 
much  lower  than  that  derived  from  the  values  calculated  on  the  basis  of 
the  isohydric  principle.  Furthermore,  it  follows  from  the  work  of  Ken- 


264        PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

dall,25  discussed  in  the  preceding  section,  that  even  polar  molecules,  such 
as  we  have  in  the  weak  acids,  are  affected  only  to  a  slight  extent  by  the 
presence  of  strong  acids.  The  depression  of  the  concentration  of  the 
un-ionized  fraction  of  a  strong  electrolyte  in  equilibrium  with  its  solid 
phase,  due  to  the  addition  of  other  electrolytes,  has  been  ascribed  to 
interaction  between  the  ions  and  the  un-ionized  fraction  of  the  first  salt, 
and  the  salting  out  effect  in  the  case  of  non-electrolytes  has  been  cited  in 
support  of  this  hypothesis.  From  the  foregoing  analysis,  however,  it 
would  appear  that  the  behavior  of  non-electrolytes,  as  well  as  that  of 
weak  electrolytes,  in  the  presence  of  strong  electrolytes,  lends  little  sup- 
port to  this  hypothesis.  On  the  whole,  it  appears  much  more  likely  that 
the  concentration  of  the  un-ionized  fraction  varies  as  a  function  of  the 
nature  of  the  added  electrolyte,  and  that,  in  general,  it  varies  less  than 
indicated  by  the  calculated  values  given  above. 

According  to  the  above  calculation,  the  ion  product  varies  consider- 
ably with  the  concentration  of  the  added  electrolyte  and  depends,  to  a 
considerable  extent,  upon  the  nature  of  this  electrolyte.  Observations 
on  the  solubility  of  salts  in  the  presence  of  other  salts  indicate  that,  even 
in  the  case  of  strong  electrolytes,  the  ion  product  remains  approximately 
constant  on  the  addition  of  other  electrolytes.26  It  is  at  once  evident 
that  if  the  concentration  of  the  un-ionized  fraction  is  only  slightly  de- 
creased on  the  addition  of  a  second  electrolyte,  the  concentration  of  the 
ions  is  appreciably  smaller  than  that  derived  from  calculations  on  the 
basis  of  the  iso-ionic  principle.  The  result  is  to  render  the  value  of  the 
ion  product  approximately  constant  and  independent  of  the  concentration 
of  the  added  electrolyte. 

As  we  have  seen,  the  conductance  of  mixtures  of  hydrochloric  acid 
and  sodium  chloride,  calculated  on  the  assumption  that  the  equilibrium 
in  the  mixture  is  governed  by  the  isohydric  principle,  is  not  in  accord 
with  the  experimentally  determined  values.  On  the  other  hand,  we  saw 
that,  in  the  more  dilute  solutions,  the  observed  values  agree  very  nearly 
with  the  values  calculated  on  the  assumption  that  in  the  mixture  the  equi- 
librium conforms  to  Equation  52.  It  is  evident  that  if  C  remains  con- 
stant in  the  mixture,  P^  will  likewise  remain  constant.  If,  therefore, 

the  concentration  of  the  un-ionized  fraction  of  a  salt  remains  constant, 
the  ion  product  should  also  remain  constant  according  to  this  principle. 
Assuming  this  principle  to  hold,  we  may  calculate  values  for  the  con- 
centration of  the  un-ionized  fraction  and  for  the  ion  product  in  the  case 
of  a  salt  in  equilibrium  with  its  solid  phase  in  the  presence  of  a  second 

**  Kendall,  Zoc.  oit. 

"Stteglitz,  J.  Am.  Chem.  Soc.  SO,  946  (1908). 


HETEROGENEOUS  EQUILIBRIA  265 

electrolyte.    For  thallous  chloride  in  the  presence  of  potassium  chloride 
the  following  results  are  obtained: 

TABLE  CV. 

VALUE  OF  THE  UN-IONIZED  FRACTION  AND  OF  THE  ION  PRODUCT  FOB 

THALLOUS  CHLORIDE  IN  WATER  AT  25°,  IN  THE  PRESENCE  OF 

POTASSIUM  CHLORIDE,  ASSUMING  EQUATION  52. 

C  of  KC1  0  25  50  100  200 

Su   0.001755      0.001746      0.001734      0.001703      0.001586 

P-X104  .  2.052  2.039  2.011  1.973  1.808 

i 

The  calculations  are  based  upon  A0  values  identical  with  those  of 
Bray  and  Winninghoff.27  Taking  into  account  the  uncertainties  in  the 
values  of  A0,  as  well  as  in  the  values  of  the  solubilities  themselves,  it- 
appears  from  an  inspection  of  the  above  table  that,  assuming  the  equi- 
librium in  the  mixture  to  be  governed  by  Equation  52,  the  concentration 
of  the  un-ionized  fraction  in  the  mixture,  as  well  as  the  value  of  the  ion 
product,  remains  substantially  constant  up  to  a  concentration  of  approxi- 
mately 0.1  N  potassium  chloride.  For  example,  in  the  presence  of  0.1  N 
potassium  chloride,  the  concentration  of  the  un-ionized  fraction  as  cal- 
culated is  0.001703  as  against  0.001755  for  a  solution  of  thallous  chloride 
in  water  alone.  This  represents  an  increase  of  only  1.9  per  cent.  Simi- 
larly, the  ion  product  over  the  same  concentration  interval  varies  ondy 
4  per  cent.  The  increase  in  the  value  of  the  ion  product  and  the  de- 
crease in  the  concentration  of  the  un-ionized  fraction  of  a  binary  salt, 
on  addition  of  a  second  electrolyte  with  a  common  ion,  is  therefore 
primarily  a  consequence  of  the  form  of  the  function  assumed  as  govern- 
ing the  equilibrium  in  the  mixture.  The  manner  in  which  P  •  and  C  vary 

%  u 

on  the  addition  of  a  second  electrolyte  remains  uncertain  so  long  as  the 
law  governing  the  equilibria  in  mixtures  remains  unknown. 

If  the  value  of  the  ion  product  and  the  concentration  of  the  un-ionized 
fraction  remain  constant,  the  solubility  of  the  salt  is  given  by  the 
equation: 

KS 
(70)  S  =  Su 

where  S  is  the  solubility  of  the  salt  at  any  concentration,  Su  is  the  con- 
centration of  the  un-ionized  fraction,  which  is  independent  of  concentra- 
tion, 20^  is  the  concentration  of  the  common  ion,  and  K^  is  a  constant 

for   the   mixture   whose   value   may   be   determined   from   the   ioniza- 

27  Bray  and   Winninghoff,  loc.   cit. 


266        PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

tion   function   of   the  pure    electrolyte.     The   value   of   2(7-  may    be 

calculated  by  means  of  Equation  52.  From  Equation  70,  it  is  evident 
that  the  total  solubility  of  the  salt  S  in  the  presence  of  another  salt  with 
a  common  ion  is  a  linear  function  of  the  reciprocal  of  the  common  ion 

concentration  ^77-.     In  Figure  52  are  plotted  solubility  values  for  T1C1 


0.016 


0.01+ 


O  012 


O-O/O 


0.00* 


0.006 


6.004 


o.o  oa 


zo 


30 


70 


Reciprocal  of  Total  Ion  Concentration  - 


FIG.  52.    Representing  the  Solubility  of  Thallous  Chloride  as  a  Function  of  the 
Reciprocal  of  the  Total  Ion  Concentration. 

in  the  presence  of  thallous  sulphate,  thallous  nitrate,  potassium  chloride 
and  barium  chloride.  In  the  case  of  KC1  as  added  salt,  the  values  of 
2C  •  have  been  calculated  according  to  Equation  52.  The  other  values 

of  2C  •  are  those  of  Bray,28  which  are  based  on  the  isohydric  principle. 
Since  the  difference  in  the  values  of  2(7^  as  derived  by  Equations  51  and 
52  is  not  great,  an  approximate  comparison  is  afforded  by  the  values 

"Bray,  J.  Am.  Chem.  Soc.  S3,  1674  (1911). 


HETEROGENEOUS  EQUILIBRIA  267 

employed.  On  examination  of  the  figure,  it  will  be  seen  that,  up  to  a 
concentration  of  0.1  N  of  added  salt,  the  points  lie  very  nearly  upon  a 
straight  line,  and,  furthermore,  that  the  solubility  values  due  to  the 
addition  of  different  electrolytes  conform  very  nearly  to  the  same  straight 
line.  It  cannot  be  said  that  Equation  70  actually  holds  for  the  mixture; 
nevertheless,  the  effect  of  different  electrolytes  upon  the  solubility  of 
thallous  chloride  is  much  more  uniform  in  character  when  treated  in  this 
way  than  when  treated  according  to  the  isohydric  principle.  Up  to 
0.1  N  concentration  of  added  salt,  the  solubilities  differ  only  a  few  per 
cent  from  the. linear  relation. 

The  conclusion  to  be  drawn,  however,  is  not  so  much  that  the  ion 
product  and  the  concentration  of  the  un-ionized  fraction  as  calculated 
according  to  Equation  52  remain  constant  for  a  salt  in  equilibrium  with 
its  solution  as  that  the  values  obtained  for  the  concentrations  of  the 
various  molecular  species  present  in  the  mixture  depend  upon  the  law 
assumed  to  govern  the  equilibrium  in  the  mixture.  The  conclusion 
reached  by  many  writers,  that  the  concentration  of  the  un-ionized  frac- 
tion decreases  greatly  with  increasing  concentration  of  the  added  electro- 
lyte,29 is  a  consequence  of  the  assumption  of  the  isohydric  principle  as 
a  basis  for  calculating  the  concentrations  of  the  various  molecular  species 
present.  As  was  shown  by  Bray  and  Hunt,30  the  specific  conductances 
of  mixtures  of  sodium  chloride  and  hydrochloric  acid,  calculated  on  the 
basis  of  the  isohydric  principle,  are  throughout  greater  than  the  measured 
ones.  It  follows,  therefore,  that  the  concentrations  of  the  ions  as  calcu- 
lated according  to  this  assumption  are  greater  than  the  true  ones.  Con- 
sequently, the  concentration  of  the  un-ionized  fraction,  which  is  obtained 
by  difference,  is  obviously  found  too  low.  It  is  not  probable  that  the 
concentration  of  the  un-ionized  fraction  of  an  electrolyte  in  equilibrium 
with  its  solutions  will  be  entirely  unaffected  by  the  addition  of  other 
electrolytes,  since,  as  we  have  seen  in  a  preceding  section,  the  solubility 
of  non-electrolytes  is  influenced  by  the  addition  of  electrolytes.  We 
might  expect,  however,  that  the  change  in  the  concentration  of  the  un- 
ionized fraction  would  not  differ  greatly  from  that  of  non-electrolytes 
under  similar  conditions.  This  conclusion  is  further  borne  out  by  the 
results  of  Kendall 31  on  the  solubility  of  organic  acids  in  the  presence  of 
other  acids. 

In  the  case  of  salts  which  are  more  soluble,  the  effect  of  a  second 
electrolyte  upon  the  solubility  is,  in  general,  much  smaller  and,  in  some 

»  Noyes,  J.  Am.  Chem.  8oc.  33,  1643  (1911)  ;  Stieglitz,  ibid..  30,  946  (1908)  :  Arrhenius. 
Ztachr.  f.  phys.  Chem.  31,  224  (1899). 

80  Bray  and  Hunt,  J.  Am.  Chem.  Soc.  33,  781    (1911). 
"Kendall,  loc.  cit. 


268        PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

cases,  the  solubility  may  even  be  increased.  The  solubility  of  certain 
salts,  such  as  silver  chloride,31*  is  greatly  increased  on  addition  of  an 
electrolyte  with  a  common  ion.  Since  it  has  been  shown  that  this  effect 
is  chiefly  due  to  the  formation  of  complex  ions,  a  discussion  of  these 
systems  may  be  omitted. 

The  solubility  of  binary  salts  is  materially  increased  on  the  addition 
of  a  salt  without  a  common  ion.  This  may  be  accounted  for  on  the 
assumption  that  metathetic  reaction  takes  place  between  the  ions  of  the 
saturating  salt  and  the  solvent  electrolyte,  the  increased  solubility  being 
due  to  the  formation  of  the  corresponding  un-ionized  molecules.  If  the 
isohydric  principle  is  assumed  to  hold  for  such  mixtures,  the  resulting 
values  obtained  for  the  ion  product  and  the  concentration  of  the  un- 
ionized salt  are  found  to  vary  with  the  concentration  of  the  added  elec- 
trolyte in  a  manner  similar  to  that  found  in  mixtures  with  a  common  ion. 
Here  again  it  is  not  possible  to  reach  a  conclusion  relative  to  the  nature 
of  the  processes  involved  with  any  considerable  degree  of  certainty. 

c.  The  Solubility  of  Salts  of  Higher  Type  in  the  Presence  of  Other 
Electrolytes.  The  solubility  relations  in  the  case  of  salts  of  higher  type 

TABLE  CVI. 

SOLUBILITY  OF  SILVER  SULPHATE  IN  WATER  AT  25°  IN  THE  PRESENCE  OF 

OTHER  ELECTROLYTES. 

Concentration  of 

Salt  Salt  Solubility 

None ....        0.00  53.52 

KN03   24.914  57.70 

49.774  61.13 

99.87  67.93 

Mg(N03)2 24.764  59.44 

49.595  64.32 

99.46  72.70 

AgN03    24.961  39.09 

49.86  28.45 

99.61  16.96 

K2S04    25.024  50.66 

50.044  49.35 

100.00  48.04 

200.03  48.30 
MgS04    20.022  52.21 

50.069  50.93 

100.04  49.95 

200.05  49.60 

'"Forbes,  J.  Am.  Chem.  Soc.  33,  1937    (1911). 


HETEROGENEOUS  EQUILIBRIA 


269 


are  much  more  complex  than  in  that  of  binary  salts  and  the  results  are 
accordingly  more  difficult  to  interpret.  A  considerable  amount  of  experi- 
mental material  exists,  much  of  which  is  due  to  Harkins.32 

In  Table  CVI  are  given  values  of  the  solubility  of  silver  sulphate  in 
water  at  25°  in  the  presence  of  different  electrolytes.  The  concentrations 
are  expressed  in  millimols,  C  X  10~3,  per  liter.  The  results  for  this,  as 
well  as  for  other  ternary  salts,  are  shown  graphically  in  Figure  53.  The 


8, 

1 
~ 


0.08 

PbCl, 

0.076 

Tl,C,Ot 
0.072 

0.068 
0.064 
0.060 

0.056 

AglS04 

0.052 

0.048 
0.044 

Ba<BrO,)f 
0.040 

0.036 
0.032 
0.028 


0.024 

0.020 

o.o  1  6 

0.012 

0.008 

0.004 

B*(IO,), 

o.o 


\ 


0.0  0.025  0.05  0.10  0.20 

Concentration  of  added  salt  in  equivalents. 

FIG.  53.    Solubility  of  Ternary  Electrolytes  in  Water  in  the  Presence   of  Other 

Electrolytes. 

results  for  lead  iodate  are  given  in  Table  CVII  and  are  shown  graphically 
in  Figure  54. 

An  examination  of  the  figures  and  the  data  given  in  the  tables  shows 
that,  in  general,  electrolytes  of  the  same  type  have  a  similar  influence 
upon  the  solubility  of  a  ternary  electrolyte.  This  is  particularly  true 

"Harkins,  /.  Am.  Ohem.  8oc.  33,  1807  (1911)  ;  <M<i.,  58,  2679  (1916). 


270        PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 


TABLE  CVII. 

SOLUBILITY  OF  LEAD  IODATE  IN  WATER  AT  25°  IN  THE  PRESENCE 
OF  OTHER  SALTS. 


Salt 

None    . . . 
Pb(N03)2 


KN03 


KIO, 


Concentration 
Salt 

0.00       •  • 

0.1 

1.0 

10.0 

100.0 

500.0 

3000.0 

2.0 

10.0 

50.0 

200.0 

0.05304  •  •  • 
0.1061 


Solubility 

•  0.1102 

•  0.087 
0.0411 
0.0185 
0.016 
0.028 
0.150 
0.1141 
0.1334 
0.2037 
0.2544 
0.0697 
0.0437 


o.oo 


KN03 


O.OOOZ  0.000+  0.0006          0.0006          0.OO/0 

Concentration  of  added  salt  in  equivalents. 
54-    Solubility  of  Lead  locjate  in  Water  in  the  Presence  of  Other  Electrolyte?. 


HETEROGENEOUS  EQUILIBRIA  271 

at  low  concentrations.  Salts  having  a  univalent  ion  in  common  with  a 
ternary  electrolyte  cause  an  initial  depression,  which,  in  many  cases,  is 
followed  by  a  slight  increase  in  the  solubility  at  higher  concentrations. 
This  latter  effect,  furthermore,  is  greatly  influenced  by  the  properties  of 
the  electrolytes  involved.  The  minimum  is  particularly  pronounced  in 
the  case  of  solutions  of  lead  chloride  in  the  presence  of  lead  nitrate. 
Salts  which  are  only  very  slightly  soluble  suffer  a  much  greater  depres- 
sion of  the  solubility  on  the  addition  of  a  salt  with  a  common  ion  than 
do  salts  of  greater  solubility.  The  addition  of  an  electrolyte  without  a 
common  ion  in  general  causes  an  increase  in  the  solubility  of  a  ternary 
salt.  This  increase  appears  to  vary  considerably  with  the  nature  of  the 
added  electrolyte.  In  the  case  of  silver  sulphate,  for  example,  the  in- 
crease in  solubility  due  to  the  addition  of  nitric  acid  is  much  greater 
than  that  due  to  the  addition  of  potassium  nitrate. 

In  the  case  of  salts  whose  solubility  is  high,  the  effect  of  an  addition 
of  various  electrolytes  depends  largely  upon  the  nature  of  the  added  salt. 
In  Table  CVIII  are  given  the  solubilities  of  strontium  chloride  in  water 

TABLE   CVIII. 

SOLUBILITY  OP  STRONTIUM  CHLORIDE  IN  THE  PRESENCE  OP  OTHER 
SALTS  IN  WATER  AT  25°. 

Equiv.  of 

added  salt  in  Sol.  equiv.  per 

Salt  added  1000  g.  H20  1000  g.  H20 

None   None  7.034 

Sr(N03)2  0.1372  7.044 

0.5766  7.038 

1.0988  7.030 

3.318  6.956 
Solid  Sr(N03)2 

NaN03 0.3621  7.198 

0.5010  7.270 

3.553  7.276 

6.856  6.844 
Solid  Sr(N03)2 

HN03  0.1771  7.028 

0.3521  7.034 

1.277  7.034 

HC1  0.1551  6.882 

0.5162  6.502 

1.017  5.996 

2.165  4.864 

9.205  0.530 


272        PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 


TABLE  CVIIL— Continued 


Salt  added 


HBr 


Equiv.  of 
added  salt  in 
1000  g.  H20 

.     0.06817 
0.4191 
0.9716 
1.154 


HI 


KI 


KC1    . 

CuCl2 
KNCX 


0.1641 
0.4462 
0.4126 
0.7539 

0.09199 
0.5401 
0.6015 
1.445 

0.0719 
0.433 
0.8576 
1.594 

0.7134 
2.276 

0.09796 
0.4755 


Sol.  equiv.  per 
1000  g.  H20 

6.974 
6.696 
6.262 
6.132 

6.890 
6.650 
6.672 
6.366 

7.034 
7.016 
7.038 
6.992 

7.016 
6.950 
6.882 
6.764 

6.812 
6.352 

7.122 

7.406 


at  25°  in  the  presence  of  different  electrolytes.  The  results  are  shown 
graphically  in  Figure  55.  It  will  be  seen  from  the  table  and  the  figure 
that,  up  to  a  concentration  of  l.ON,  the  solubility  effects  are,  in  general, 
small.  The  difference  between  the  effect  of  salts  with  and  without  a  com- 
mon ion  is  not  great.  The  solubility  of  strontium  chloride  remains  prac- 
tically constant  on  addition  of  nitric  acid,  potassium  iodide,  and  stron- 
tium nitrate.  The  addition  of  potassium  chloride  causes  a  slight 
decrease  in  solubility,  while  that  of  sodium  nitrate  causes  a  slight  in- 
crease. The  greatest  decrease  in  solubility  results  from  the  addition  of 
hydrochloric  acid,  but  it  is  to  be  noted  that  hydriodic  acid  and  hydro- 
bromic  acid,  which  do  not  have  an  ion  in  common  with  strontium  chloride, 
cause  almost  as  great  a  solubility  depression  as  does  hydrochloric  acid. 
It  is  clear  that,  at  high  concentrations,  the  solubility  effects  are  not  to  be 
ascribed  primarily  to  ionic  interaction.  The  relationships  between  the 
solubility  effects  resemble  those  obtained  in  the  case  of  solutions  of  non- 
electrolytes  in  the  presence  of  electrolytes. 

In  the  Table  CIX  are  given  values  for  the  solubility  of  lanthanum 


HETEROGENEOUS  EQUILIBRIA 


273 


iodate  in  the  presence  of  different  electrolytes  in  water  at  25°,  as  meas- 
ured by  Harkins  and  Pearce.33  The  results  are  shown  graphically  in 
Figure  56.  It  will  be  observed  that  the  solubility  of  lanthanum  iodate 
is  markedly  decreased  on  the  addition  of  a  salt  with  a  common  univalent 
ion.  The  addition  of  a  salt  with  a  common  trivalent  ion  causes  a  slight 
initial  decrease  in  solubility,  followed  by  an  increase  at  higher  concentra- 


0  /  2.  5  4-567  *. 

Equivalents  of  added  salt  per  1000  g.  water. 

FIG.  55.    Solubility  of  Strontium  Chloride  in  Water  in  the  Presence  of  Other 

Electrolytes. 

tions.    On  the  addition  of  a  salt  without  a  common  ion,  there  is  a 
marked  increase  in  the  solubility  throughout. 

While  the  solubility  of  different  salts  is  in  general  affected  in  a 
similar  manner  on  the  addition  of  other  salts,  provided  the  solubility  is 
relatively  low,  the  interpretation  of  the  experimental  results  is  ren- 
dered uncertain,  owing  to  the  fact  that  the  ionization  functions  for  the 
electrolytes  in  the  mixtures  are  not  known.  At  the  same  time,  it  is  pos- 
sible that,  in  the  case  of  salts  of  higher  type,  intermediate  ions  are  present 
as  a  result  of  which  it  not  only  becomes  difficult  to  take  into  account 

"  Harkins  and  Pearce,  J.  Am.  Chem.  Soc.  38,  2679  (1916). 


274       PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 


TABLE  CIX. 

SOLUBILITY  OP  LANTHANUM  IODATE  IN  WATER  AT  25°  IN  THE  PRESENCE 
OF  OTHER  ELECTROLYTES. 


Salts  added 
La(N03)3   ... 


KI03 


NaIOa 


NaN03 


Milli-normal 

cone,  salt 

solution 


La(N08)3.2NH4NCX 


0.0 

2.0 

5.0 

10.0 

50.0 

100.0 

200.5 

0.0000 
0.0990 
0.4957 
0.9914 
1.9828 

0.0000 
0.0913 
0.4560 
0.9130 
1.8260 
3.6530 
4.5326 
6.7989 

0.0 

25.0 

50.0 

100.0 

200.0 

400.0 

800.0 

1600.0 

3200.0 

0.00 

26.34 

52.68 

105.36 

158.04 

196.83 

393.67 

787.35 

1574.70 


in 


Solubility 
millimols 

1.0301 
0.8430 
0.7968 
0.7825 
0.8320 
0.9362 
1.1195 

1.0301 
0.9476 
0.8488 
0.7488 
0.5632 

1.0301 
0.9572 
0.8507 
0.7658 
0.6016 
0.2973 
0.2017 
0.1468 

1.0301 
1.3092 
1.4921 
1.7481 
2.0873 
2.4657 
3.2487 
4.3114 
4.5657 

1.0301 
0.9510 
1.0156 
1.1367 
1.2303 
1.3061 
1.6016 
2.0551 
2.8968 


HETEROGENEOUS  EQUILIBRIA 


275 


the  effect  of  the  intermediate  ion,  but,  in  addition,  the  concentration  of 
the  intermediate  ion  cannot  be  determined  with  any  degree  of  certainty, 
even  in  solutions  in  pure  water.  Nevertheless,  as  Harkins  has  pointed 
out,  the  solubility  curves  may  be  accounted  for  in  a  general  way  on  the 
assumption  that  intermediate  ions  are  present  in  solutions  of  electrolytes 
of  higher  type. 


0,0/Z 


ao      o-t        o*       0.3       0.4      of      0.6       0.7       o*       o>9 

Concentration  of  added  salt  in  equivalents  per  liter. 

FIG.  56.    Solubility  of  Lanthanum  lodate  in  Water  in  the  Presence  of  Other 

Electrolytes. 

It  will  be  sufficient  to  consider,  here,  the  solubility  of  a  ternary  elec- 
trolyte of  the  type  MX2,  which  ionizes  according  to  the  equation: 


As  we  have  already  seen  in  connection  with  the  solubility  of  binary  elec- 
trolytes in  the  presence  of  other  electrolytes,  the  experimental  results 
in  the  case  of  fairly  dilute  solutions  are.  in  reasonably  good  agreement 
with  the  assumption  that  the  concentration  of  the  un-ionized  fraction 
of  the  salt,  as  well  as  the  ion  product,  remains  constant  on  the  addition 
of  other  electrolytes.  If  a  similar  assumption  is  made  in  the  case  of  a 
ternary  electrolyte,  it  leads  to  the  following  equations  for  the  solubility 
of  the  salt  in  the  presence  of  an  electrolyte  with  a  common  univalent  ion, 
a  common  divalent  ion,  and  without  a  common  ion. 
With  a  common  univalent  ion, 


(71) 


S- 

- 


where  K  is  the  ionization  constant  of  the  reaction  given  above.     In  this 
equation  the  solubility  appears  as  an  explicit  function  of  the  concentra- 


276       PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

tion  of  the  common  ion  X~.  In  order  to  determine  the  concentration  of 
the  common  ion  in  the  mixture,  it  is  obviously  necessary  to  know  the 
ionization  functions  for  the  various  electrolytes  concerned.  While  these 
functions  are  not  known,  a  fair  approximation  could  probably  be  obtained 
by  assuming  one  of  the  functions  given  in  Chapter  IX.  This  would 
necessarily  involve  the  further  assumption  that  intermediate  ions  are  not 
present. 

On  the  addition  of  a  common  divalent  ion,  the  solubility  is  given  by 
the  equation: 


(7*\ 

I'2)  —  2  M++  > 

while,  on  the  addition  of  a  salt  without  a  common  ion, 

M~Y- 
"»  --  ~'  —  ' 


where  Kf  is  the  constant  of  the  reaction 

MY2  =  M"  +  2Y-. 

Since  different  electrolytes  of  the  same  type  are  ionized  to  practically 
the  same  extent  in  water,  it  follows  that,  in  the  mixture  containing  a 
salt  without  a  common  ion,  the  equivalent  concentrations  X~  and  M++ 
will  not  differ  greatly  from  each  other.  The  first  two  terms  of  Equation 
73,  therefore,  will  remain  constant  on  the  addition  of  a  salt  without  a 
common  ion.  The  last  term  of  this  equation,  however,  will  obviously 
increase  as  the  concentration  of  the  ion  Y~,  due  to  the  addition  of  a  salt 
NY,  increases.  It  is  evident,  therefore,  that  according  to  this  equation 
the  solubility  of  a  ternary  salt  should  be  increased  upon  the  addition  of  a 
salt  without  a  common  ion.  On  the  other  hand,  comparing  Equations  71 
and  72,  it  is  evident  that  the  addition  of  a  common  univalent  ion  will 
cause  a  much  greater  solubility  depression  than  will  the  addition  of  a 
common  divalent  ion,  since  the  concentration  of  the  univalent  ion  appears 
in  the  denominator  with  the  exponent  2,  while  that  of  the  divalent  ion 
appears  in  the  denominator  with  the  exponent  %.  Roughly,  this  is  in 
agreement  with  observations.  As  may  be  seen  by  reference  to  Figure  53, 
the  addition  of  a  salt  with  a  common  univalent  ion  causes  a  much  greater 
depression  than  does  the  addition  of  a  salt  with  a  common  divalent  ion. 

As  we  have  already  seen,  the  solubility  of  a  binary  salt  decreases  as 
the  reciprocal  of  the  concentration.  of  the  common  ion.  The  solubility 
curve  of  a  binary  electrolyte,  therefore,  should  lie  intermediate  between 


HETEROGENEOUS  EQUILIBRIA  277 

that  of  a  ternary  electrolyte  in  the  presence  of  a  common  univalent  ion 
and  in  that  of  a  common  divalent  ion. 

Harkins34  has  calculated  solubility  curves  on  the  assumption  that 

(74)  Sm  (S  +  C)n  =  1, 

where  ra  and  n  are  the  number  of  ions  resulting  from  the  dissociation, 
while  S  is  the  solubility  of  the  salt  and  C  is  the  concentration  of  the 
added  salt.  The  curves  calculated  on  these  assumptions  correspond 
roughly  with  the  observed  curves.  An  exact  correspondence  is  not  to  be 
expected,  since  the  assumptions  made  in  calculating  these  curves  are 
obviously  only  roughly  fulfilled. 

The  equations  given  above  obviously  do  not  account  for  the  form  of 
the  curves  at  higher  concentrations,  particularly  for  the  increase  in  the 
solubility  of  a  ternary  salt  on  the  addition  of  larger  amounts  of  a  salt 
with  a  common  divalent  ion.  According  to  Harkins  this  increase  is  due 
to  the  formation  of  an  intermediate  ion  MX*  according  to  the  reaction: 

M«  +  X-  =  MX*. 

On  this  assumption  the  solubility  on  the  addition  of  a  salt  with  a  com- 
mon univalent  ion  is  given  by  the  equation: 

(75)  S 


where  K^  is  the  constant  resulting  from  the  reaction: 

MX*  +  X-  =  MX2. 

It  is  evident,  from  this  equation,  that,  if  intermediate  ions  MX*  are 
formed,  then,  on  the  addition  of  an  electrolyte  NX,  the  solubility  depres- 
sion will  be  smaller  than  in  the  case  where  no  intermediate  ions  are 
formed.  From  this  equation,  it  follows,  also,  as  may  readily  be  seen 
by  differentiating  with  respect  to  the  concentration  of  the  common  ion 
X",  that  with  increasing  concentration  the  solubility  must  decrease  irre- 
spective of  the  values  of  the  constants  K  and  K±. 

If  a  salt  of  the  type  MY2  is  added,  the  solubility  is  given  by  the 
equation: 


(76)  S  =  MX,  +  XM 


Here  K2  is  the  equilibrium  constant  resulting  from  the  reaction: 

M++  +  X-  =  MX+. 

"Harkins,  Joe.  cit. 


278        PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

It  is  evident  that: 

(77)  K  =  K1K2. 

An  inspection  of  the  above  equation  shows  that,  owing  to  the  formation 
of  the  intermediate  ion  MX+,  the  value  of  whose  concentration  is  given 
by  the  second  term  of  the  right-hand  member,  the  solubility  is  increased 
due  to  the  formation  of  the  intermediate  ion.  With  increasing  value  of 
M++,  this  term  may  become  sufficiently  great  to  overbalance  the  effect 
of  the  last  term  of  the  right-hand  member.  This  is  more  readily  seen  on 
differentiating  Equation  76  with  respect  to  the  concentration  of  the 
common  ion  M++,  which  leads  to  the  equation  : 

tm  dS      _£y*MX2W    1          1    \ 

dM++"       M++%     \2K2     2M+V* 

The  solubility  will  be  a  minimum  when: 
(79)  1 


Obviously,  the  concentration  of  the  common  divalent  ion  M++  at  the 
minimum  point  of  the  solubility  curve  is  equal  to  the  equilibrium  con- 
stant K2.  If  this  constant  is  small,  then  the  minimum  point  will  lie  at  a 
low  concentration;  whereas,  when  this  constant  is  large,  the  minimum 
•point  will  lie  at  high  concentrations.  In  other  words,  when  K2  is  large 
the  fraction  of  salt  present  in  the  form  of  intermediate  ions  MX+  is 
relatively  small;  whereas  when  Kz  is  small  this  fraction  is  relatively 
large  and  the  minimum  point  accordingly  appears  at  low  concentrations. 
It  may  be  noted,  in  this  connection,  that  the  solubility  curves  of  lead  salts 
exhibit  a  pronounced  minimum  at  relatively  low  concentrations.  That 
for  lead  iodate  in  the  presence  of  lead  nitrate  is  in  the  neighborhood  of 
0.04  N  ;  that  for  lead  chloride  in  the  presence  of  lead  nitrate  is  at  approxi- 
mately the  same  concentration.  Silver  sulphate,  in  the  presence  of  potas- 
sium sulphate,  exhibits  a  minimum  in  the  neighborhood  of  0.1  N.  Cal- 
cium sulphate  exhibits  minima  in  the  neighborhood  of  0.15  N  in  the 
presence  of  salts  with  a  common  S04~~  ion.  In  the  case  of  salts  with  a 
common  Ca+*  ion,  this  minimum  does  not  appear.  The  difference  in  the 
behavior  of  calcium  sulphate  in  the  presence  of  a  common  positive  or 
negative  divalent  ion  may  be  due  to  various  causes,  since  in  this  case 
there  is  involved  the  formation  of  two  different  types  of  complexes. 
Considering  the  behavior  of  uni-divalent  salts,  it  is  evident  that  those 
salts  which  exhibit  a  pronounced  tendency  to  form  complexes,  such  as 
lead  salts  for  example,  likewise  exhibit  a  pronounced  minimum  in  the 
solubility  curve  in  the  presence  of  a  common  divalent  ion. 


HETEROGENEOUS  EQUILIBRIA  279 

The  simple  explanation  offered  above  must  obviously  not  be  pressed 
too  far,  particularly  in  the  more  concentrated  solutions.  On  the  addi- 
tion of  a  salt  of  the  type  MY2,  there  is  a  possibility  that  complexes  of 
the  form  MXY  may  result.  In  all  likelihood,  however,  at  low  concen- 
trations, these  are  not  present  to  a  large  extent. 

While  solutions  of  highly  soluble  salts,  as  well  as  solutions  of  non- 
electrolytes,  exhibit  a  great  variety  of  properties  which  bring  out  clearly 
the  individual  characteristics  of  the  various  substances  involved,  in  solu- 
tions of  difficultly  soluble  salts,  the  solubility  curves  show  remarkable 
regularities,  indicating  that  the  observed  behavior  of  these  solutions  lies 
in  properties  common  to  electrolytes  in  general,  at  these  concentrations. 
The  solubility  effects  are  readily  explained  on  the  assumption  that  the 
concentration  of  the  un-ionized  fraction,  as  well  as  the  ion  product, 
remains  substantially  constant  on  the  addition  of  a  second  electrolyte. 
The  great  decrease  in  the  concentration  of  the  un-ionized  fraction,  which 
many  investigators  have  assumed  to  be  correct,  is  doubtful.  It  appears 
probable  that  this  result  follows  from  a  failure  of  the  applicability  of 
the  isohydric  principle  to  mixtures  of  electrolytes.  The  solubility  in- 
crease observed  in  the  case  of  salts  of  higher  type  on  the  addition  of 
salts  with  a  common  polyvalent  ion  makes  it  appear  probable  that 
intermediate  ions  are  present  in  relatively  large  amounts  in  solutions  of 
salts  of  higher  type  at  higher  concentrations. 

Heterogeneous  equilibria  from  a  thermodynamic  point  of  view  will 
be  discussed  in  another  chapter. 


Chapter  XI. 
Other  Properties  of  Electrolytic  Solutions. 

1.  The  Diffusion  of  Electrolytes.  If  a  concentration  gradient  exists  in 
an  electrolytic  solution,  diffusion  will  take  place.  The  rate  of  diffusion 
of  an  ion  is  the  greater  the  greater  its  mobility.  However,  in  view  of 
the  fact  that  the  ions  of  an  electrolyte  are  oppositely  charged,  the  dif- 
fusion of  these  ions  will  not  be  independent  of  one  another.  Nernst1 
has  derived  an  expression  for  the  diffusion  coefficient  in  dilute  solutions 
of  electrolytes.  The  diffusion  coefficient  is  thus  given  by  the  equation: 


(80) 


D  = 


2UV 

u  +  v 


XRT, 


in  which  U  and  V  are  the  ionic  mobilities.  If  the  electrolyte  is  not 
completely  ionized,  the  neutral  molecules  also  will  diffuse,  and  their  rate 
of  diffusion  will,  in  general,  differ  from  that  of  the  ions.  The  diffusion 
coefficient  of  various  electrolytes  has  been  measured  by  Arrhenius  and 
more  extended  measurements  are  due  to  Oholm.2  In  Table  CX  are  given 
values  for  the  diffusion  coefficients  of  different  electrolytes  in  water  at  18°. 

TABLE  CX. 

DIFFUSION  COEFFICIENTS  OF  ELECTROLYTES  IN  WATER  AT  18°. 


Cone. 

NaCl 

KOI 

LiCl 

KJ 

HOI  CH2COOH 

NaOH 

KOH 

0.01  .... 

....  1 

.170 

1 

.460 

1.000 

1.460 

2 

.324 

0.930 

1.432 

1.903 

0.02  .... 

1 

.152 

1 

.431 

0.980 

1.428 

2 

.285 

0.910 

1.404 

1.889 

0.05  .... 

....  1 

.139 

1 

.409 

0.971 

1.412 

2 

.251 

0.895 

1.386 

1.872 

0.10  .... 

....  1 

.117 

1 

.389 

0.951 

1.391 

2 

.229 

0.884 

1.364 

1.854 

0.20  .... 

1 

.098 

1 

.367 

0.929 

1.380 

2 

.202 

0.871 

1.342 

1.843 

0.50  

....  1 

.077 

1 

.345 

0.919 

1.372 

2 

.188 

0.856 

1.310 

1.841 

1.00  

....  1 

.070 

1 

.330 

0.920 

1.366 

2.217 

0.833 

1.290 

1.855 

2.00  

1 

.320 

0.928 

.  . 

.  , 

.  . 

1.259 

1.892 

2.8  

....  1.064 

1.434 

t 

3.6  

1 

.338 

,  . 

,  . 

.  . 

t  . 

9  , 

>  > 

4.2  

.  . 

0.956 

.  . 

.  . 

.  . 

.  . 

,  . 

5.5  

1 

.065 

.  . 

.  . 

1.549 

.  . 

.  . 

.  . 

.  . 

» Nernst,  Ztschr.  f.  phi/a.  Chem.  2,  613   (1888). 

» Oholm,  Ztachr.  }.  phya.  Chem.  50,  309  "(1905);  Meddel.   Vet.-Akad's.  Nobelinstitut, 
Vol.  «,  No.  22  (1911). 

280 


OTHER  PROPERTIES  OF  ELECTROLYTIC  SOLUTIONS  281 

It  will  be  observed  that  in  the  more  dilute  solutions  the  diffusion 
coefficient  is  the  greater,  the  greater  the  conductance  of  the  electrolyte. 
Thus,  at  0.01  normal,  the  diffusion  coefficient  of  HC1  is  2.324,  of  KOH 
1.903,  of  KC1  1.460,  and  of  LiCl  1.000.  As  the  concentration  increases, 
the  diffusion  coefficient  in  the  more  dilute  solutions  decreases.  This  may 
be  accounted  for  if  we  assume  that  as  the  concentration  increases  the 
ionization  decreases,  and  that  the  diffusion  coefficient  of  the  neutral 
molecules  is  smaller  than  that  of  the  ions.  At  higher  concentrations  the 
influence  of  viscosity  change  must  be  taken  into  account.  In  the  case 
of  most  salts,  the  viscosity  increases  with  increasing  concentration,  and 
it  is  to  be  expected  that,  owing  to  this  factor,  there  will  be  a  decrease  in 
the  diffusion  coefficient  at  higher  concentrations.  The  increase  in  the 
value  of  the  diffusion  coefficient  at  very  high  concentrations  cannot  be 
accounted  for  in  this  way.  If,  however,  the  ions  are  hydrated,  then  it  is 
not  improbable  that  at  the  higher  concentrations,  where  the  number  of 
salt  molecules  becomes  comparable  with  that  of  the  number  of  water 
molecules,  the  degree  of  hydration  of  the  ions  decreases,  as  a  result  of 
which  their  mobilities  may  be  expected  to  increase. 

Of  particular  significance  are  the  results  obtained  by  Arrhenius8 
for  the  diffusion  of  electrolytes  in  the  presence  of  other  electrolytes.  If 
the  diffusing  electrolyte  has  a  rapidly  and  a  slowly  moving  ion,  the  dif- 
fusion of  the  rapidly  moving  ion  is  hindered,  owing  to  the  drag  exerted 
upon  it  by  the  charge  on  the  more  slowly  moving  ion.  If,  now,  another 
electrolyte  is  added,  the  rate  of  diffusion  of  the  first  electrolyte  will  be  in- 
creased, since  the  diffusion  of  the  oppositely  charged  ion  may  be  compen- 
sated by  the  diffusion  of  another  ion  in  the  opposite  direction.  For  exam- 
ple, the  diffusion  coefficient  of  a  0.52  N  solution  of  HC1  in  water  at  12° 
is  2.09,  while  that  of  the  same  electrolyte  in  3.43  N  solution  of  NH4C1  is 
4.67,  and  in  a  0.375  N  solution  of  KC1  3.89.  Evidently,  on  adding  am- 
monium chloride  to  the  hydrochloric  acid  solution,  the  rate  of  diffusion 
is  greatly  increased  due  to  the  fact  that  the  motion  of  the  Cl~  ions  in  the 
direction  of  the  concentration  gradient  is  compensated  by  a  motion  of  the 
NH4+  ions  in  the  opposite  direction.  This  phenomenon  is  quite  general, 
as  may  be  seen  from  Table  CXI. 

The  influence  of  the  added  electrolyte  on  the  diffusion  coefficient  is 
extremely  marked.  For  example,  the  addition  of  0.028  N  KC1  to  a  1.04  N 
solution  of  HC1  raises  the  diffusion  coefficient  from  a  value  of  2.09  to  2.27, 
or  approximately  ten  per  cent.  Effects  such  as  these  afford  perhaps  the 
strongest  grounds  we  have  for  believing  that  electrolytes  are  ionized. 
On  the  other  hand,  they  do  not  enable  us  to  determine  to  what  extent 

•Arrhenius,  Ztschr.  /.  phyg.  Chem.  10,  51   CL892). 


282        PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 


TABLE  CXI. 

DIFFUSION  COEFFICIENTS  OF  ELECTROLYTES  IN  THE  PRESENCE  OF  OTHER 
ELECTROLYTES  IN  WATER  AT  12°. 


Diffusing 
Electrolyte 
1.04-n  HC1 


0.52-n  HC1 


0.55-n  HNCX 


0.54-n  NaOH 


0.98-n  KOH 


0.49-n  KOH 


Added 
Electrolyte 

None 

0.67-n  NaCl 
0.1-n  NaCl 
0.75-n  KC1 
0.25-n  KC1 
0.085-n  KC1 
0.028-n  KC1 
0.75-n  BaCl2 
0.085-n  BaCl2 
2-n  NH4C1 
0.25-n  NH4C1 

None 

0.042-n  KC1 
0.375-n  KC1 
3.43-n  NH4C1 

None 

0.1-n  KN03 
0.5-n  KN03 
0.5-n  NaNOs 

None 

0.25-n  NaCl 
0.067-n  NaCl 
0.25-n  Na2S04 
1-n  NaN03 
1-n  NaC2H302 
0.2-n  NaN03 
0.2-n  NaC2H30, 
3-n  NaCl 
1-n  NaCl 

None 

0.1-n  KC1 
1-n  KC1 

None 

0.05-n  KN03 
0.5-n  KN03 
0.5-n  KC1 


Diffusion 

Coefficient 

at  12° 

2.09 

3.51 

2.50 

4.22 

3.08 

2.51 

2.27 

4.12 

2.46 

4.50 

2.99 

2.09 
2.46 
3.89 
4.67 

1.91 
2.59 
3.70 
3.39 

1.15 
1.90 
1.51 
1.80 
2.20 
1.78 
1.80 
1.60 
1.98 
2.30 

1.72 
1.92 
2.57 

1.70 
1.91 
2.54 
2.57 


ionization  has  taken  place  in  a  given  solution.  These  facts,  while  they 
do  not  enable  us  to  distinguish  between  partial  and  complete  ionization, 
supply  abundant  evidence  that  salts  are  ionized  to  a  large  extent. 


OTHER  PROPERTIES  OF  ELECTROLYTIC  SOLUTIONS  283 

2.  Density  of  Electrolytic  Solutions.  According  to  the  ionic  theory, 
the  properties  of  dilute  solutions  of  electrolytes  are  additive  functions  of 
the  concentrations  of  the  ions  and  of  the  un-ionized  molecules.  If  Ji  is 
the  value  of  a  given  property  of  such  solutions  and 

(81) 
then: 
(82)  kn  =  Ay  +  B(l  —  Y), 


where  Jt0  is  the  value  of  the  property  at  zero  concentration,  jc  is  its  value 
at  the  concentration  C,  y  is  the  ionization  of  the  electrolyte  at  this  con- 
centration, and  A  and  B  are  constants  relating  to  the  ions  and  the  un- 
ionized molecules  respectively.  Ajt  is  evidently  the  percentage  equivalent 
property  change  due  to  the  electrolyte  at  the  concentration  in  question. 
In  applying  this  equation,  it  is  tacitly  assumed  that  the  property  is  inde- 
pendent of  any  interaction  between  the  ions  and  the  un-ionized  molecule, 
otherwise  a  term  should  be  added  involving  the  concentration  and  the 
equation  would  no  longer  be  linear.  Equation  82  may  evidently  be 
written: 

(83)  Arc  =  B  +  A'y, 
where 

(84)  A'  =  A  —  B. 

Ajt  is  thus  a  linear  function  of  y,  and  from  the  known  values  of  An  the 
values  of  y  may  be  obtained.  Such  additive  properties  lend  themselves 
to  a  determination  of  YJ  and  a  comparison  with  the  value  of  y  as  derived 
from  conductance  measurements  might  be  expected  to  thus  serve  as  a 
check  on  the  correctness  of  these  values.  A  simpler  method  of  com- 
parison consists  in  plotting  the  measured  values  of  A:t  against  those  of  y 
as  derived  from  conductance  measurements.4  If  the  two  methods  yield 
concordant  values  of  y,  the  graph  should  be  a  straight  line. 

Unfortunately,  this  method  of  checking  the  results  of  conductance 
measurements  is  restricted  in  its  application  owing  to  the  fact  that  in 
many  cases  the  value  of  a  given  property  for  the  un-ionized  fraction  does 
not  differ  appreciably  from  the  sum  of  those  of  its  constituent  ions.  This 
appears  to  be  the  case,  for  example,  with  many  of  the  optical  properties 
of  electrolytic  solutions. 

Many  properties  of  atomic  and  molecular  complexes  depend  upon  the 

*  «  Heydweiller,  Ann.  d.  Phya.  37,  739  (1912)  ;  ibid.,  SO,  873  (1909)  ;  Magie,  Physical 
Kevvew  25,  171  (1907). 


284        PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

number  and  the  distribution  of  the  charges  within  these  complexes.  If 
these  complexes  are  relatively  stable,  as  we  know  the  ion  complex  to  be, 
then  the  properties  of  the  complexes  will  be  relatively  independent  of  the 
manner  in  which  two  or  more  of  them  are  grouped  together.  We  should 
not,  therefore,  expect  any  considerable  change  in  those  properties  of  elec- 
trolytes which  depend  primarily  upon  the  distribution  of  the  charges  on 
the  ions;  for  the  ionic  complexes  exist  practically  unchanged  in  the 
un-ionized  molecules  whatever  their  state;  that  is,  whether  in  solution  or 
as  liquid,  solid,  or,  perhaps,  even  vapor.  Only  such  properties  as  depend 
on  the  field  due  to  the  ions  may  be  expected  to  exhibit  a  marked  differ- 
ence for  the  ions  and  the  un-ionized  molecules.  In  the  un-ionized  state 
the  two  ions  form  an  electrical  doublet  with  a  closed  field,  while  in  the 
ionized  state  the  field  is  open.  Those  properties,  therefore,  which  depend 
upon  the  field  in  the  immediate  neighborhood  of  the  ions  should  give  evi- 
dence of  the  existence  of  the  ions  and  of  the  un-ionized  molecules,  should 
these  molecules  be  present  in  solution. 

Foremost  among  the  properties  of  this  class  we  should  expect  the  den- 
sity of  solutions  to  be  included.  It  is  well  known  that  the  solution  of 
salts  in  water  is  accompanied  by  a  marked  volume  contraction,  which  is 
the  greater  the  lower  the  concentration  of  the  solution.  According  to 
Drude  and  Nernst,5  a  volume  change  is  to  be  expected  as  a  result  of 
the  action  of  the  ionic  charge  on  the  molecules  of  the  surrounding 
medium.  Obviously,  other  effects  may  come  into  play,  such  as  the  hydra- 
tion  of  the  ions,  etc. 

The  density  of  aqueous  solutions  has  been  studied  from  this  point  of 
view  by  Heydweiller.6  He  found  that,  with  a  few  exceptions,  the  density 
change  of  electrolytic  solutions  may  be  represented  as  a  linear  function 
of  the  ionization  corresponding  to  Equation  82.  It  is  true  that  the  pre- 
cision of  the  density  measurements  is  not  always  great  and  often  the 
concentration  range  over  which  the  equation  has  been  tested  is  not  large. 
Then,  again,  the  lowest  concentrations  up  to  which  the  relation  has  been 
tested  is  not  much  below  0.1  N.  It  is  a  remarkable  fact,  however,  that 
for  a  number  of  electrolytes  the  density  may  be  expressed  as  a  linear 
function  of  the  ionization  over  large  concentration  ranges,  as,  for  example, 
in  the  case  of  zinc  chloride,  calcium  chloride  and  potassium  hydroxide. 

The  constant  B  is  the  equivalent  percentage  density  change  due  to  the 
un-ionized  salt.  If  it  be  assumed  that  the  un-ionized  molecules  in  the 
solution  occupy  the  same  volume  as  they  do  in  the  pure  condition  as  salts, 
then  the  value  of  the  constant  B  may  be  calculated  from  the  known  den- 

•  Drude  and  Nernst,  Ztschr.  f.  pJiys.  Chem.  15,  79  (1894). 

•  Heydweiller,  loc.  cit. 


OTHER  PROPERTIES  OF  ELECTROLYTIC  SOLUTIONS  285 

sity  of  the  salt.  In  Table  CXII  are  given  values  of  BC,  so  calculated, 
together  with  values  of  B&  as  experimentally  determined  by  Heydweiller 
for  different  salts  in  water. 

TABLE    CXII. 

COMPARISON  OF  EXPERIMENTAL  AND  CALCULATED  VALUES  OF  B. 
Salt  Be  Bc  Salt  Be  BC 

NH4I  8.38  8.55                 LiN03  3.71  4.02 

NaCl   3.36  3.15                 LiCl   2.06  2.17 

NaN03    4.88  4.74                 Nal   10.45  10.77 

KN03    5.21  5.30  1/2  CaI2  ....  11.55  11.70 

1/2  K2S04   . ..  5.73  5.45  1/2  BaBr2  . . .  11.80  11.75 

KC103 6.73  7.00                 1/2  BaI2 15.56  15.58 

AgN03 13.28  13.04  1/2  CdN03  . .  9.21  9.15 

From  an  inspection  of  the  table  it  appears  that  the  values  of  Be  and 
#  are  in  remarkably  good  agreement.  The  differences  probably  do  not 

G 

exceed  the  experimental  error.  The  values  calculated  in  this  way,  how- 
ever, do  not  in  all  cases  agree  as  well  as  those  appearing  in  the  above 
table.  In  the  case  of  salts  which  show  a  marked  tendency  to  form 
hydrates,  Heydweiller  has  employed  the  density  of  the  hydrated  salt 
rather  than  that  of  the  anhydrous  salt  and  has  obtained  excellent  agree- 
ment between  the  observed  and  the  calculated  values  of  the  constant  B, 
while  in  another  group  of  electrolytes  the  values  of  B  as  calculated  are 
not  in  close  agreement  with  those  as  measured.  This  is  illustrated  in  the 
following  table. 

TABLE   CXIII. 

COMPARISON  OF  EXPERIMENTAL  AND  CALCULATED  VALUES  OF  B. 
Salt  Bp  Br  Salt  fl  fl 

\j  c 

NH4C1   0.42  1.83                 KC1  2.94  3.71 

NH4Br 4.45  5.69                 KBr 6.65  7.48 

NH4NO, 2.60  3.39                 KI   10.56  11.20 

1/2  N2H8S04  .  2.49  2.87                 KCNS    3.70  4.57 

Lil 9.53  10.10  1/2  K2Cr04  . .  5.83  6.16 

LiBr 5.84  6.19                 RbCl 6.24  7.79 

CsCl 10.36  12.62 

While  there  is  a  marked  deviation  between  the  values  of  B  as  derived 
from  the  experimental  curves  and  as  calculated  from  the  density  of  these 


286       PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 


salts,  nevertheless,  the  parallelism  existing  between  the  two  sets  of  values 
is  unmistakable. 

The  constants  A  are  the  equivalent  percentage  density  changes  due 
to  the  ions.  This  property  should  be  an  additive  one.  If  this  is  true, 
the  difference  in  the  values  of  the  constant  A  for  salts  with  a  common 
ion  should  be  constant.  Heydweiller  has  calculated  the  value  of  the 
constants  A  for  different  ions.  To  illustrate  how  nearly  the  additive 
condition  is  fulfilled  by  the  experimental  values  of  the  constants,  the  fol- 
lowing values  are  given.  Table  CXIV-A  relates  to  a  series  of  sodium 
salts  and  Table  CXIV-B  to  a  series  of  nitrates.  In  the  first  column  is 
given  the  symbol  of  the  negative  ion  of  the  salt,  in  the  second  column  the 
experimentally  determined  value  of  the  constant  A,  in  the  third  column 
the  value  of  the  constant  Aa  for  the  anion,  and  in  the  last  column  the 


difference  A  —  Aa  = 


for  the  cation. 
similar  values  are  given  for  those  salts. 


In  the  case  of  the  nitrates 


A. 

C2H302  . 
F  

Sodium  Salts 
A          Aa 

4.44        3.04 
4.56        3.16 
7.33        5.95 
5.95        4.54 
4.38        3.02 
8.08        6.68 
11.52      10.27 
4.88        3.40 
7.09        5.77 
7.72        6.38 

C103  .... 
N03  .... 
Cl  

Br  

I  

OH  

1/2  S04  . 
1/2  Cr04 

TABLE    CXIV, 
SHOWING  THE  ADDITIVE  NATURE  OF  A. 


1.40 
1.40 
1.38 
1.41 
1.36 
1.40 
1.25 
1.48 
1.32 
1.34 


Mean      1.38 


H   .... 

B.    Nit 
A 

.  .     347 

.rates 
Aa 

—  1.05 
—  0.35 
1.38 
10.02 
—  0.98 
2.10 
6.32 
1.33 
3.61 
5.43 
3.63 
2.02 
4.38 
6.54 
10.34 

Li  

.  .     420 

Na   ... 

.  .     5.95 

Ag  .... 

..   14.61 

NH4  ., 
K   

.  .     3.61 
.  .     6  72 

Rb   ... 

.  .   10.75 

1/2  Mg 
1/2  Zn 
1/2  Cd 
1/2  Cu 
1/2  Ca 
1/2  Sr 
1/2  Ba 
1/2  Pb 

.     5.82 
..     8.09 
..    9.94 
.,    8.14 
.,    6.57 
.  .     8.98 
.  .(10.76). 
.  .  14.87 

4.52 
4.55 
4.57 
4.59 
4.59 
4.62 
4.43 
4.49 
4.48 
4.51 
4.51 
4.55 
4.60 
(4.22) 
4.53 


Mean      4.54 


It  will  be  noted  that  the  values  of  the  constants  A    and  Aj  show  remark- 

CL  K, 

ably  small  variations.    They  thus  fulfill  the  condition  of  additivity. 
Only  a  few  electrolytes,  such  as  magnesium  sulphate,  sodium  car- 


OTHER  PROPERTIES  OF  ELECTROLYTIC  SOLUTIONS          287 

bonate,  and  sulphuric  acid,  exhibit  density  changes  which  do  not  vary 
as  linear  functions  of  the  ionization.  The  cause  of  the  variation  in  these 
cases  is  uncertain,  but  may  be  due  to  the  formation  of  complex  ions,  to 
hydrolysis,  etc. 

The  volume  changes  of  electrolytic  solutions  in  methyl  alcohol  have 
likewise  been  examined.7  The  results  obtained  correspond  very  closely 
with  those  obtained  in  the  case  of  aqueous  solutions.  The  density  change 
due  to  ionization,  which  is  obviously  equal  to  the  difference  A  —  B,  is 
considerably  greater  in  methyl  alcohol  solutions  than  it  is  in  water.  This 
is  not  surprising,  since  the  dielectric  constant  of  this  solvent  is  much 
smaller  than  that  of  water.  We  should  expect  that,  if  the  density  change 
is  the  result  of  the  action  of  the  field  due  to  the  charge  on  the  surrounding 
solvent  molecules,  the  density  change  would  be  the  greater  the  smaller 
the  dielectric  constant  of  the  medium. 

In  order  to  finally  establish  the  additive  nature  of  the  density  changes 
of  electrolytic  solutions,  it  will  be  necessary  to  extend  the  measurements 
to  much  lower  concentration.  Methods  exist  for  measuring  the  densities 
of  dilute  solutions  with  sufficient  precision  to  make  it  possible  to  extend 
the  measurements  to  concentrations  approaching  10~3  N.  Until  this  is 
done,  the  results  of  density  measurements  must  remain  more  or  less  in 
doubt.  The  concordance  of  the  results  so  far  obtained,  however,  would 
appear  to  justify  further  efforts  along  these  lines. 

Some  measurements  have  been  made  by  Rohrs8  on  the  density  of 
solutions  in  ethyl  alcohol  and  acetone.  The  interpretation  of  the  results 
is  uncertain  owing  to  the  small  change  in  the  ionization  over  the  con- 
centration intervals  for  which  measurements  were  made. 

3.  Velocity  of  Reactions  as  Affected  by  the  Presence  of  Ions.  The 
speed  of  many  reactions,  such  as  the  inversion  of  sugars  and  the  hydroly- 
sis of  esters,  for  example,  is  greatly  increased  on  addition  of  acids. 
Ostwald  9  showed  that  the  catalytic  effect  of  different  acids  is  the  greater 
the  stronger  the  acid.  It  appeared,  at  first,  that  the  catalytic  effect  of  the 
acids  provided  an  independent  method  for  estimating  the  concentration 
of  the  hydrogen  ions  in  an  acid  solution.  Further  investigations,10  how- 
ever, showed  that  the  catalytic  action  is  likewise  dependent  upon  other 
factors,  such  as  the  presence  of  other  substances  and  especially  electro- 
lytes. Thus,  the  catalytic  action  due  to  a  strong  acid  should  be  reduced 
on  the  addition  of  a  salt  of  this  acid.  While  such  a  reduction  takes  place 

7  Ruthenberg,  Inaugural  Dissertation,  Rostock   (1913). 

•Rohrs,  Ann.  d,  Phys.  57,  289   (1912). 

9  Ostwald.  J.  prakt.  Chem.  28,  449   (1883)  ;  29,  385   (1884)  ;  31,  307   (1885). 

"Arrhenius,  Ztschr.  f.  phys.  CJiem.  5,  1  (1890). 


288        PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

in  the  case  of  the  weaker  acids,  in  that  of  the  stronger  acids  the  catalytic 
action  is  actually  increased. 

It  is  now  commonly  accepted  that  the  un-ionized  acid  molecules,  as 
well  as  the  ions  themselves,  influence  the  rate  of  these  reactions.  Ac- 
cording to  this  hypothesis,  the  reaction  constant  is  given  by  an  equation 
of  the  form: 

(85)  K  =  KiCh+KnCn, 

where  K^  and  Kn  are  the  velocity  constants  for  the  ions  and  the  un-ion- 
ized molecules  respectively  and  C^  and  Cn  are  the  concentrations  of  the 
ions  and  the  un-ionized  molecules.  The  constant  Kn  is  in  general  deter- 
mined by  adding,  to  a  dilute  solution  of  an  acid,  a  salt  of  the  same  acid. 
Under  these  conditions,  the  ionization  of  the  acid  is  practically  repressed 
to  zero  and  it  is  assumed  that  the  residual  catalytic  action  is  due  entirely 
to  the  un-ionized  acid  molecules.  The  results  of  many  experiments  on  a 
great  variety  of  reactions  are,  on  the  whole,  in  good  accord  with  this 
hypothesis.  It  should  be  noted,  however,  that  the  ratio  of  the  constants 
Kn  to  K-  is  a  function  of  the  strength  of  the  acid,  as  well  as  of  other 

factors.  The  weaker  the  acid,  the  smaller  is,  in  general,  the  value  of  this 
ratio.  In  the  case  of  the  strong  acids,  the  value  of  this  ratio  may  be 
unity  or  even  greater. 

In  the  following  table  are  given  values  of  the  inversion  coefficient  for 
aqueous  solutions  of  cane  sugar,  according  to  Ostwald,  at  25°.  The 
concentration  of  the  acids  was  in  all  cases  0.5  N  and  the  values  given  for 
the  constants  are  relative  to  that  of  hydrochloric  acid  taken  as  unity.  t 

TABLE    CXV. 
INVERSION  COEFFICIENTS  FOR  DIFFERENT  ACIDS. 

Hydrochloric  acid 1.000  Trichloroacetic  acid 0.754 

Nitric  acid 1.000  Dichloroacetic  acid  0.271 

Chloric  acid 1.035  Monochloroacetic  acid   . . .  0.0484 

Sulphuric  acid 0.536  Formic  acid 0.0153 

Benzenesulphonic  acid 1.044  Acetic  acid 0.0040 

It  is  clear  that  the  catalytic  action  of  the  acids  is  intimately  related 
to  their  strength. 

For  the  purpose  of  investigating  the  effect  of  the  neutral  molecules 
upon  reactions,  solutions  in  non-aqueous  solvents  are  in  many  respects 
better  adapted  than  those  in  water,  since  the  ionization  of  the  acid  in 


OTHER  PROPERTIES  OF  ELECTROLYTIC  SOLUTIONS  289 

these  solutions  is  much  smaller  than  in  water.    Numerous  experiments 
have  therefore  been  carried  out  in  methyl  and  ethyl  alcohols. 

In  the  following  table  are  given  values  of  the  esterification  constant 
for  different  acids  in  methyl  alcohol,  according  to  Goldschmidt  and 
Thueson,11  at  25°.  The  numerical  values  for  0.05  HC1,  0.1  picric  acid 
and  0.1  trichlorobutyric  acid  are  given  in  the  second,  third  and  fifth 
columns  respectively,  while  in  the  fourth  and  sixth  columns  are  given 
the  values  for  picric  acid  and  trichlorobutyric  acid  of  the  strength  given 
in  the  presence  of  0.15  picrate  and  0.1  butyrate  respectively. 

TABLE    CXVI. 

ESTERIFICATION  CONSTANTS  IN  METHYL  ALCOHOL  FOB  DIFFERENT  ACIDS 
IN  THE  PRESENCE  OF  OTHER  ACIDS  AS  CATALYZERS. 

Catalyzing  acids 
Esterifying  acid  HC1    C6H3N307      Picrate    C4C13H602   Butyrate 

Phenylacetic  acid  . .  2.23  0.265  0.047  0.0167  0.00102 

Acetic  acid 4.86  0.590  0.100  0.0375  0.00172 

n-Butyric  acid 2.23  0.277  0.0535  0.0177  0.00097 

i-Butyric  acid 1.55  0.196  0.0353  0.0129  0.00074 

i-Valeric  acid   0.583  0.0735  0.00144  0.00475  0.00029 

From  this  table  it  may  be  seen  that  the  catalytic  action  of  an  acid 
is  the  greater  the  stronger  the  acid.  Nevertheless,  the  catalytic  action 
of  an  acid  is  not  proportional  to  the  concentration  of  the  hydrogen  ion. 
The  ratio  between  the  velocity  constants  for  0.05  N  hydrochloric  acid 
and  0.1  N  picric  acid  varies  between  7.78  and  8.91  for  the  different  acids, 
while  the  ratio  of  the  ion  concentrations  is  6.56.  So,  also,  the  ratio  of 
the  hydrogen  ion  concentrations  for  0.1  N  and  0.01  N  picric  acid  is  3.64. 
The  ratio  of  the  esterification  constants  between  these  concentrations  is 
3.90.  It  will  be  observed  that,  on  the  addition  of  sodium  picrate  to  picric 
acid,  the  velocity  constant  varies  approximately  in  the  ratio  of  1  to  6, 
while,  on  the  addition  of  trichlorobutyrate  to  butyric  acid,  the  velocity 
constant  changes  in  the  ratio  of  1  to  18.  It  should  be  stated  in  this  con- 
nection that  the  values  given  for  the  constants  of  picric  acid  and  tri- 
chlorobutyric acid  in  the  presence  of  other  salts  represent  practically  the 
minimum  limiting  values  which  are  independent  of  the  concentration  of 
the  added  salt.  In  other  words,  the  salt  added  is  sufficient  to  completely 
repress  the  ionization  of  the  acid.  Accordingly,  the  residual  catalytic 
action  of  the  acid  must  either  be  due  to  the  un-ionized  molecule  or  to 
some  other  agency.  The  weaker  the  acid,  the  smaller,  relatively,  is  the 

"Goldschmidt  and  Thueson,  Ztschr.  f.  phya.  Chem.  81,  30  (1913). 


290       PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

catalytic  power  of  the  neutral  molecule.    The  values  of  the  constants 
K-  and  K    may  be  determined  from  a  series  of  measurements.     In  the 

case  of  the  examples  given  above  the  following  values  of  K^C^  were 

obtained  for  trichlorobutyric  acid  as  catalyzer  at  concentrations  of  0.1 
and  0.05  N. 

TABLE   CXVII. 

VELOCITY  COEFFICIENTS  FOR  THE  HYDROGEN  ION  OF  TRICHLOROBUTYRIC 
ACID  IN  THE  ESTERIFICATION  OF  DIFFERENT  AdDS. 

Con- 
centration   Phenyl- 
of  Acid        acetic  Acetic         n-Butyric        i-Butyric        i-Valeric 

0.1   0.0157  0.0358  0.0167  0.0122  0.00448 

0.05 0.0109  0.0247  0.0114  0.00826  0.00304 

Ratio  ....     1.44  1.45  1.47  1.48  1.47 

It  is  seen  that  the  ratio  of  the  velocity  coefficients  calculated  for  the 
ions  between  0.1  and  0.05  N  is  1.46.  According  to  conductance  measure- 
ments the  ratio  of  the  ionization  of  this  acid  at  these  two  concentrations 
is  1.42.  Taking  into  account  the  numerous  possible  sources  of  error,  the 
agreement  appears  fairly  satisfactory. 

Kn 

In  the  following  table  are  given  values  of  K    and  — -  for  hydrochloric 

K* 

acid,  acetic  acid,  and  the  chloro-  substitution  products  of  this  acid.12 

TABLE  CXVIII. 

T7- 

VARIATION  OF  THE  RATIO  -=^  FOR  DIFFERENT  ACIDS. 

Ki 

Acid    |  *»        x?  **     1 

Hydrochloric   acid    780  1.77  

Dichloroacetic  acid 220  0.50  5.1  X  10'2 

a-p-Dibromopropionic  acid 67  0.152  1.67  X  10~2 

Monochloroacetic  acid 24.5  0.055  0.155  X  10'2 

Acetic  acid 1.5  0.0034  0.0018  X  10'2 

Similar  results  have  been  obtained  by  Taylor  and  by  Ramstedt.13    It  is 
clear  that  the  value  of  Kn  increases  with  the  strength  of  the  acid.    As 

"Dawson  and  Fowls,  J.  Ghent.  Soc.  10&  2135   (1913). 

"Taylor,  Meddel  K.  Vet.-Akad's.  Nvbelinstitut,  Vol.  3,  No.  1  (1913)  ;  Ramste<Jt,  ibid., 
Vol.  Jj  No.  7  (1015). 


OTHER  PROPERTIES  OF  ELECTROLYTIC  SOLUTIONS  291 

shown  in  the  table,  the  catalytic  action  of  the  neutral  molecule  of  hydro- 
chloric acid  is  greater  than  that  of  the  hydrogen  ion.  As  the  acids  become 
weaker,  however,  the  catalytic  activity  of  the  neutral  molecule  diminishes 
and  reaches  very  low  values  in  the  case  of  weak  acids.  According  to 

Kn 

Taylor,  the  ratio  -=—  is  related  to  the  ionization  constant  of  the  acid  by 

Ki 
the  equation: 

(86) 

where  A  is  a  constant.  If  the  law  of  mass  action  applies  to  the  acid,  this 
leads  to  the  relation: 


where  (7    and  C  -  are  the  concentrations  of  the  un-ionized  and  the  ionized 

u  i/ 

fractions  of  the  acid,  respectively. 

Many  reactions  are  likewise  catalyzed  by  the  hydroxyl  ions  and,  in 
alcohol  solutions,  by  the  alcoholate  ion.1*  Since  the  results  obtained  in 
these  cases  do  not  differ  materially  from  those  obtained  in  the  case  of 
acids,  the  details  need  not  be  given  here. 

It  is  evident  that  the  catalyjbic  action  of  the  hydrogen  and  hydroxyl 
ions  may  not  be  safely  employed  for  determining  ion  concentrations.  At 
all  events,  the  interpretation  of  the  results  obtained  is  still  very  uncertain. 
In  this  connection,  it  may  be  noted  that  Arrhenius16  has  proposed  an 
alternative  hypothesis  to  account  for  the  effect  of  the  un-ionized  fraction 
according  to  which  the  change  in  the  catalytic  activity  is  a  secondary 
effect  due  to  a  change  in  the  osmotic  pressure  of  the  molecules  as  a 
consequence  of  the  addition  of  the  neutral  salt.  While  the  catalytic 
effects  due  to  the  ions  are  of  great  interest  and  often  of  much  practical 
importance,  nevertheless,  at  the  present  time,  they  have  not  enabled  us 
to  gain  any  great  insight  into  the  nature  of  electrolytic  solutions. 

Recently  a  number  of  investigators  have  ascribed  the  effect  of  neutral 
salts  on  the  catalytic  action  of  strong  acids  to  the  influence  of  the  added 
salt  on  the  thermodynamic  potential;  or,  what  is  equivalent,  the  activity 
of  the  hydrogen  ion.  Harned  16  has  studied  the  action  of  neutral  salts  on 
the  rate  of  various  reactions  which  are  catalyzed  by  ionic  catalysts  and 
has  compared  this  effect  with  the  change  in  the  activity  of  the  catalyzing 

"Acree,  numerous  articles  in  the  Am.  Chem.  J.  and  J.  Am.  CJiem.  Soc.  since  1907. 
See:  Acree,  Am.  Chem.  J.  49,  474  (1913). 

"Arrhenius  and  Andersson.  Meddel  K.  Vet.-Akad'a.  Nobclinstitut  3,  No.  25   (1917). 
«•  Harned,  J.  Am.  Chem.  Soc.  40,  1461   (1918). 


292       PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

ions  due  to  the  addition  of  another  salt  with  a  common  ion.  He  finds, 
in  general,  a  correspondence  between  the  two  effects.  Harned  has  also 
pointed  out  that  the  neutral  salt  effect  appears  to  be  related  to  the  hydra- 
tion  of  the  added  salt. 

Akerlof 17  has  measured  the  influence  of  acids  on  the  rate  of  reaction 
of  ethyl  acetate  in  water  at  20°  in  the  presence  of  varying  concentrations 
of  salts  having  an  ion  in  common  with  the  acid.  The  activity  of  the 
hydrogen  ion  in  the  presence  of  an  added  salt  was  determined  by  meas- 
urement of  the  electromotive  force  of  concentration  cells.  With  hydro- 
chloric and  sulphuric  acids,  Akerlof  found  that,  with  increasing  activity 
of  the  hydrogen  ion,  the  velocity  constant  increases.  For  the  same  con- 
centration of  the  catalyzing  acid,  the  velocity  constant  Kr  was  found  to 

increase  approximately  as  the  cube  root  of  the  activity  of  the  hydrogen 
ion;  or, 

(87)  K    = 


where  Kf  is  the  velocity  constant  of  the  reaction,  A  is  a  constant  having 

the  same  value  for  different  salts,  and  a  is  the  activity  of  the  hydrogen 
ion  in  the  mixture.  In  the  case  of  a  number  of  salts  the  value  of  A  was 
found  to  depend  upon  the  nature  of  the  salt  as  well  as  upon  its  concen- 
tration. It  is  possible  that  these  discrepancies  are  due  to  various  sources 
of  error.  With  increasing  acid  concentration,  the  constant  A  was  found 
to  increase,  but  apparently  not  in  direct  proportion  to  the  concentration. 

Equation  87  is  an  empirical  one,  and,  so  long  as  it  lacks  a  theoretical 
foundation,  the  interpretation  of  the  foregoing  results  remains  uncertain. 
It  appears  that,  for  a  number  of  salts,  the  velocity  constant  varies  in  a 
similar  manner  with  the  activity  of  the  catalyzing  ion;  but,  in  view  of 
the  possible  exceptions  which  have  been  found,  it  would  be  unsafe  to 
generalize  the  results  obtained.  Further  investigations  along  this  line, 
however,  are  of  considerable  interest. 

4.    Optical  Properties  of  Electrolytic  Solutions.    Among  the  various 
optical  properties  of  solutions,  only  the  absorption  spectra  have  been 
determined  with  sufficient  precision  to  make  it  possible  to  draw  conclu- 
sions with  any  degree  of  certainty.    Since  the  optical  properties  are  pri 
marily  dependent  upon  the  number  and  arrangement  of  the  electrons 
it  is  not  to  be  expected  that  the  ions  and  the  un-ionized  molecules  wil 
exhibit  any  marked  difference  with  respect  to  these  properties.     It  is  tru 
that,  in  the  case  of  a  few  solutions,  such  as  the  copper  salts  for  example 
marked  changes  take  place  in  the. optical  properties  as  the  concentration 

"Akerlof,  Ztschr.  f.  phys.  Chem.  98,  360   (1921). 


OTHER  PROPERTIES  OF  ELECTROLYTIC  SOLUTIONS  293 

changes,  but  these  changes  are  to  be  ascribed,  primarily,  to  a  displace- 
ment of  the  hydration  equilibrium  existing  in  these  solutions.  As  the 
solutions  become  more  dilute,  this  effect  disappears.  The  absence  of  any 
difference  in  the  optical  effects  of  the  ions  and  of  the  un-ionized  molecules 
has  led  some  writers  to  infer  that  un-ionized  molecules  are  entirely  want- 
ing in  electrolytes.  This  inference,  however,  does  not  appear  to  be  well 
founded. 

In  general,  if  no  reaction  takes  place  which  tends  to  alter  the  nature 
of  the  chromophore  group,  the  absorption  of  an  ion  is  independent  of  the 
nature  of  the  solution,  as  well  as  that  of  other  ions  with  which  it  may  be 
combined.  This  is  well  illustrated  in  the  case  of  the  absorption  of  acetic 
acid  in  the  ultra-violet  region. 

In  Figure  57  is  shown  the  absorption  curve  for  acetic  acid 18  in  water 
and  in  petroleum  ether  and  for  the  potassium  and  barium  salts  of  this 
acid  in  water.  From  an  inspection  of  the  figure  it  is  evident  that  the 
absorption  of  these  solutions  is  the  same  within  the  limits  of  experimental 
error.  In  Figure  58  is  shown  the  absorption  curve  for  ammonium,  potas- 
sium, barium  and  calcium  salts  of  trichloroacetic  acid  in  water.19  Here, 
again,  it  is  evident  that  the  absorption  curves  are  identical  within  the 
limits  of  the  experimental  error.  What  holds  true  in  the  cases  which 
have  just  been  cited  holds  true  also  in  solutions  of  other  electrolytes.  In 
general,  whenever  a  variation  arises  in  the  absorption  curve,  as  a  result 
of  a  change  in  the  solvent  or  a  change  in  the  accompanying  ion,  this 
effect  may  be  ascribed  to  some  reaction  taking  place  in  these  solutions 
which  alters  the  nature  of  the  chromophore  group. 

In  the  following  table  are  given  the  extinction  coefficients  for  chromic 
acid  and  potassium  bichromate  in  water  according  to  the  measurements 
of  Hantzsch.20 

TABLE   CXIX. 

EXTINCTION  COEFFICIENTS  OF  CHROMIC  ACID  AND  POTASSIUM 
BICHROMATE  IN  WATER. 

H2Cr207  K2Cr207 

Wave  Lengths       405      436      486       543          405      436      486        546 

10 1.9  1.73 

100 89  1.8  ..        291      88.7      1.67 

500 333      275         ..  ..  ..        292      86.8 

1000 320      269      88.5  . .  332      287      87.2 

"Hantzsch,  Ztschr.  f.  phyg.  Chem.  86.  629   (1914). 

19  Idem,  loc.  cit. 

*>Idem,  Ztschr.  f.  phys.  Chem.  63,  370   (1908). 


294       PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 


Wave  Length. 
3660         700          800         SCO 


100 
80 

SO 

31,6 
25 
20 
16 

12,6 
10 
S 
43 
S 

+ 

I 

1 

,xo 

4- 

X 

+ 

t 
1 

0 
1 

• 

• 

•f 

Wave  Length. 
4000         100  200          300         4400 


100 


so 


€3,1 


SO 


20 


16 


12.6 


10 


FIG.    57.    Absorption    Curve    of    Tri-     FIG.   58.    Absorption   Curves   of  Aqueous 


chloroacetic  Acid  in  Water(. )  and 
in  Petroleum  Ether  (X),  and  of  Po- 
tassium Trichloroacetate  in  Water 
(+),  and  Barium  Trichloroacetate  in 
Water(o)  as  a  Function  of  the  Wave 
Length. 


Solutions    of    NH4(.),    K(-f),    Ba(X), 
and  Ca(o)   Trichloracetates. 


OTHER  PROPERTIES  OF  ELECTROLYTIC  SOLUTIONS  295 

It  will  be  observed,  from  this  table,  that  the  values  of  the  extinction 
coefficients  for  chromic  acid  and  potassium  bichromate  are  identical 
within  the  limits  of  experimental  error.  The  absorption  here  is  due  to 
the  negative  ion.  It  will  be  noted  that  the  absorption,  moreover,  is 
independent  of  the  concentration,  which  indicates  that  the  negative  ion 
in  the  un-ionized  molecules  possesses  the  same  optical  properties  as  in  its 
free  state;  that  is,  in  its  conducting  state.  The  absorption  coefficients  of 
the  chromate  ion  are  not  affected  by  the  presence  of  acid,  but  they  are 
slightly  affected  by  the  presence  of  bases.  In  the  following  table  are 
given  values  of  the  extinction  coefficients  for  potassium  bichromate  in 
the  presence  of  varying  amounts  of  potassium  hydroxide  for  the  wave 
length  X  =  486. 

TABLE    CXX. 

ABSORPTION  COEFFICIENTS  OF  SOLUTIONS  OF  POTASSIUM  BICHROMATE  IN 
THE  PRESENCE  OF  POTASSIUM  HYDROXIDE. 

Wave  Length  A  =  486. 

Cone.  Base  0  1/2000  1/100  1/1 

f  50  89.9  84.3  83.7  81.7 

V 100  89.0  84.0  83.0  82.3 

[200  89.0  83.6  82.0  81.4 

It  will  be  observed  that,  on  the  addition  of  potassium  hydroxide,  the 
absorption  of  potassium  bichromate  is  affected  to  a  small  but  measurable 
extent.  Hantzsch  has  shown  that  this  is  due  to  the  formation  of  other 
chromophore  groups. 

In  different  solvents,  the  chromates  have  identical  values  of  the  ab- 
sorption coefficients,  as  may  be  seen  from  the  following  table. 

TABLE    CXXL 

ABSORPTION  COEFFICIENTS  OF  SODIUM  CHROMATE  IN  METHYL 
ALCOHOL  AND  IN  WATER. 

A,  =  486. 
V  H20  CH3OH 

2000  229  231 

5000  227  233 

The  results  obtained  from  a  study  of  other  chromophore  groups  are 
similar  to  those  obtained  in  the  case  of  the  chromates,  and  need  not  be 
given  here. 


296        PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

Hantzsch  21  has  also  studied  the  absorption  of  salts  of  certain  organic 
chromophore  groups.  In  certain  of  these  salts,  marked  changes  have 
been  found  and  Hantzsch  has  been  able  to  show  that  in  these  cases  the 
change  is  due  to  a  shift  in  the  equilibrium  between  two  chromophore 
groups.  In  the  case  of  salts  of  certain  organic  chromophores,  however, 
small  differences  have  been  found  for  which  an  adequate  explanation  has 
not  thus  far  been  given.22  In  the  following  table  are  given  values  for  the 
equivalent  extinction  coefficients  for  different  salts  of  acetyloxindon. 

TABLE   CXXII. 

EXTINCTION  COEFFICIENTS  FOR  DIFFERENT  SALTS  OF  ACETYLOXINDON 

IN  WATER. 

X  =  436. 

Concentration:        1/100   1/250   1/1250   1/2500  1/5000 
Thickness  of  layer:     1  mm.   1  cm.    2  cm.    5  cm.   10  cm. 

Sr  .      .........     400     388     390     384 

Li  ............  ..   ..     347     350     358     350 


Salt 


Na  ..............  388     385     390     382     380 

Cs  ..............  383     391     387     380     390 

Tl  ...............  389     385     381     390     394 


In  aqueous  solutions,  the  absorption  spectra  of  the  different  salts  of  this 
acid  are  very  nearly  identical  with  the  exception  of  the  lithium  salt, 
whose  values  appear  to  be  a  little  low.  In  the  case  of  all  salts,  the  extinc- 
tion coefficient  is  independent  of  the  concentration. 

While  the  extinction  coefficients  for  the  oxindon  salts  in  aqueous  solu- 
tions are  the  same  for  all  cations,  with  the  possible  exception  of  lithium, 
in  solutions  in  ethyl  alcohol  a  marked  difference  has  been  found.  In  Table 
CXXII  are  given  values  of  the  extinction  coefficients  of  different  salts  in 
ethyl  alcohol.  It  will  be  observed  that  here,  again,  the  value  of  the  co- 
efficient is  independent  of  the  concentration,  but  that  it  varies  with  the  na- 
ture of  the  positive  ion.  This  variation  is  unquestionably  far  in  excess  of 
any  probable  experimental  error.  The  difference  might  be  ascribed  to  a 
difference  in  the  optical  properties  of  the  un-ionized  molecules,  and  it  is 
known  that  in  these  solutions  the  ionization  of  these  salts  is  relatively  low. 
However,  over  the  concentration  ranges  in  question,  the  ionization  for  a 
given  salt  varies  considerably,  which  makes  it  difficult  to  account  for  the 
constancy  of  the  coefficient  at  different  concentrations.  While  Hantzsch  is 

»  Hantzsch,  Ber.  43,  82  (1910). 

Ztfic/w.  /.  phya.  Chem.  8}f  321  (1913). 


OTHER  PROPERTIES  OF  ELECTROLYTIC  SOLUTIONS  297 

TABLE  CXXIII. 

EXTINCTION  COEFFICIENTS  FOB  SALTS  OF  ACETYLOXINDON  AT  DIFFERENT 
CONCENTRATIONS  IN  ETHYL  ALCOHOL. 

X  =  436. 

Concentration:                   1/100  1/1000  1/1000  1/2500  1/5000 

Thickness:                          1cm.  1cm.  2cm.  5cm.  10cm. 

Ca  .  214  220  226            217 

Sr 230  227  232            231 

Ba 230  238  240            236 

Li  259  263  255  250            258 

a 325  330  328  325            322 

K 339  338  333  325            340 

Rb 329  327  329  343            341 

Cs   390  409  393  383            395 

Tl 325  328  337            330 

inclined  to  account  for  these  variations  on  the  basis  of  a  slight  rearrange- 
ment in  the  chromophore  group,  somewhat  similar  to  that  established  in 
the  case  of  the  salts  of  the  oximidoketones,  a  thoroughly  satisfactory  ex- 
planation of  this  behavior  of  the  above  solutions  does  not  exist. 

From  the  foregoing,  it  appears  that,  in  solutions  of  salts  which  have 
stable  chromophores,  the  absorption  spectra  are  independent  of  the  con- 
dition of  the  salt,  and  accordingly  we  may  conclude  that,  whether  an  ion 
is  combined  or  uncombined,  the  absorption  spectrum  remains  unchanged. 
Where  changes  occur,  reactions  are  to  be  looked  for,  the  nature  of  which, 
however,  has  not  been  established  in  all  cases. 

5.  The  Electromotive  Force  oj  Concentration  Cells.  The  properties 
of  a  solution  are  determined  by  the  values  of  the  variables  which  fix  its 
state.  If  the  solution  is  subject  to  the  action  of  external  forces,  its  prop- 
erties will  vary  accordingly.  Under  such  conditions  the  thermodynamic 
potential  of  the  dissolved  substance  suffers  a  change  and  electromotive 
forces  naturally  arise  under  suitable  arrangement  of  solutions  and  elec- 
trodes. Such,  for  example,  is  the  case  when  solutions  are  subjected  to 
centrifugal  action.23  We  shall,  however,  confine  ourselves  here  to  a  con- 
sideration of  electromotive  forces  arising  as  a  result  of  concentration  dif- 
ference. Wherever  we  have  a  surface  of  discontinuity  between  two 
electrolytes,  or  between  an  electrolyte  and  a  metal,  an  electromotive 
force  will  in  general  arise. 

For  a  system  under  the  action  of  external  forces,  the  condition  for 

«•  Tolman,  Proo.  Am.  Acad.  tf,  109  (1910). 


298        PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

equilibrium  requires  that  the  total  potential  shall  be  the  same  throughout 
the  system.  The  total  potential  is  defined  by  the  equation: 

(88)  M'  =  M  +  P, 

where  M'  is  the  total  potential  of  a  given  molecular  species,  M  is  its 
thermodynamic  potential,  and  >P  is  the  potential  due  to  the  external 
forces.  The  thermodynamic  potential  may  be  expressed  as  a  function  of 
the  concentration  by  means  of  the  equation: 

(89)  M  =  RTlogC  +  i  +  J, 

where  i  is  a  function  independent  of  concentration,  while  J  is  a  function 
which,  in  general,  involves  all  the  independent  variables  of  the  system. 
For  a  concentration  cell  operating  between  the  concentrations  Cx  and 
C2,  we  have: 

(90)  (M+  +  M-)  2  —  (M+  +  M-)  ±  =  —  W, 

where  M+  and  M~  are  the  thermodynamic  potentials  of  the  ions  of  a 
given  electrolyte  and  W  is  the  work  performed  by  the  cell  when  one 
equivalent  (or  mol)  of  the  electrolyte  is  carried  from  the  first  solution  to 
the  second.  Introducing  Equation  89,  and  writing  for  W  its  value  in 
electrical  units,  we  have: 

(91)  -rEF  =  RT  log£^  +  (2J.)2-  (27^, 

Uj  O1 

where  2,7-  =  J+  +  J~>  F  is  the  electrochemical  equivalent,  E  the  elec- 
tromotive force,  and  r  the  number  of  equivalents  of  electricity  flowing 
per  equivalent  of  electrolyte  transferred.  The  value  of  r  depends  upon 
the  number  of  charges  v  associated  with  a  molecule  of  the  electrolyte 
and  the  nature  of  the  electrode  process.  For  a  concentration  cell  with 
transference, 

(92)  '  r  —  v/N, 

where  N  is  the  transference  number  of  the  ion  to  which  the  electrodes 
are  impermeable.  For  cells  without  transference,  N  =  1.  The  electro- 
motive force  E  is  that  due  to  the  transfer  of  the  electrolyte  alone,  and, 
if  other  processes  are  involved,  the  measured  electromotive  force  must 
be  corrected  for  these  processes  before  introducing  into  Equation  91. 
At  higher  concentrations,  in  view  of  the  fact  that  the  ions  are  hydrated, 
solvent  will  be  carried  from  a  solution  of  one  concentration  to  that  of 
another.  This  process  involves  work  and  the  electromotive  force,  as 
measured,  must  be  corrected  accordingly.  In  general,  since  the  relative 


OTHER  PROPERTIES  OF  ELECTROLYTIC  SOLUTIONS  299 

hydration  of  the  ions  is  not  known  at  the  concentrations  in  question, 
such  corrections  cannot  be  made.  The  same  considerations  hold  true  of 
the  reactions  in  which  the  electrolyte  is  concerned,  such  as  the  formation 
of  intermediate  or  complex  ions,  complex  molecules,  etc. 

The  electromotive  force  of  a  concentration  cell  may  likewise  be 
expressed  in  terms  of  the  concentrations  of  the  un-ionized  fraction,  which 
leads  to  the  equation: 

(93)  -rEF  =  RTloS^+J^-JUi. 

If  the  conditions  of  dilute  systems  are  fulfilled,  then: 

(94)  J*  =  J-  =  Ju  =  Q, 

in  which  case  the  electromotive  force  of  the  cell  may  be  calculated,  if  the 
concentration  of  the  ions  or  of  the  un-ionized  molecules  is  known. 
Equation  93,  in  this  case,  reduces  to: 

(95) 

This  is  the  equation  first  developed  by  Nernst.24 

When  the  conditions  for  a  dilute  system  are  no  longer  fulfilled,  the 
function  J  is  involved  in  the  expression  for  the  electromotive  force.  This 
function  thus  measures  the  change  in  the  potential  of  the  electrolyte  due 
to  interaction  between  the  various  molecular  species  present  in  the 
mixture.  The  form  of  this  function  is  not  known,  except  in  so  far  as  it 
has  been  determined  experimentally.  The  electromotive  force  of  concen- 
tration cells  has  in  many  cases  been  employed  for  this  purpose,  since 
it  affords  a  convenient  and  direct  measure  of  the  change  in  the  potential 
of  the  electrolyte.  In  order  to  determine  the  true  form  of  the  function, 
however,  it  is  necessary  to  know  the  concentrations  C+  and  C"  or  C  . 

Except  as  the  concentration  of  the  ions  may  be  determined  from  con- 
ductance measurements,  no  method  appears  to  be  available  whereby  the 
concentrations  of  the  ions  and  of  the  un-ionized  molecules  in  an  electro- 
lytic solution  may  be  determined. 

For  practical  purposes,  the  equation  is  often  written: 

C  Q2 
(96)  —  rEF  =  RT  log  ^  +  ZJ^  —  27  . 

«Nernst,  Ztachr.  f.  phya.  (Them.  2t  613   (1888). 


300        PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

If  the  electromotive  forces  have  been  determined  experimentally,  they 
may  be  expressed  as  a  function  of  the  total  salt  concentration  Cg  by 

means  of  this  equation.    In  this  case,  the  function  «/,&i   includes  not  only 

the  change  in  the  potential  of  the  electrolyte  due  to  the  internal  forces 
of  the  system,  but  it  also  includes  a  term  which  takes  into  account  the 
change  in  the  expression  due  to  the  substitution  of  GS  for  C+  and  C~. 

The  electromotive  force  of  concentration  cells  for  a  great  many  elec- 
trolytes has  been  measured  by  various  investigators.25  Only  a  few 
examples  of  the  results  obtained  will  be  given  here  to  show,  in  a  general 
way,  the  manner  in  which  the  potential  of  an  electrolyte  varies  with  the 
concentration.  In  Table  CXXIV  are  given  values  of  the  electromotive 
force  of  concentration  cells  with  hydrochloric  acid  as  electrolyte  between 
silver  chloride  electrodes.26  The  concentration  of  the  concentrated  solu- 
tion is  in  this  case  throughout  0.1  N.  The  concentration  of  the  dilute 
solution  is  given  in  the  first  column,  in  the  second  column  is  given  the 
value  of  the  electromotive  force  as  measured,  in  the  third  and  fourth 

C  •          C 
columns  are  given  the  values  ~  and  -~,  as  determined  from  conduc- 

S2          C^2 

tance  measurements,  and  in  the  fifth  and  sixth  columns  the  values  of  the 
same  ratios  as  calculated  from  Equations  93  and  96,  assuming  ,7  =  0. 

TABLE  CXXIV. 

ci        cu 

COMPARISON  OF  VALUES  OF  — -  AND  — —  FOE  HC1  AS  DERIVED  FROM 

Liz  C^2 

CONDUCTANCE  AND  ELECTROMOTIVE  FORCE  MEASUREMENTS. 

(Cal.)  (Cal.) 

Cii  CUi  Ci!  Cu1 

Concentration  —  ^—  -^-  ^— 

of  dilute  sol.  E.M.F.               Li2  ^uz  Li*  Luz 

0.02  0.07617              4.78  7.76  4.57  20.9 

0.01  0.10913               9.49  17.3  8.82  77.7 

0.002  0.18711  46.7  112.5  41.8  1744.0 

ci 

It  will  be  observed  that  the  calculated  values  of  the  ratio  ~  do  not 

Ciz 
differ  greatly  from  those  derived  from  conductance  measurements,  but 

"Linhart,  J.  Am.  Chem.  Soc.  39,  2601  (1917)  ;  ibid.,  Ifl,  1175  (1919)  ;  Ellis,  ibid., 
S8,  737  (1916)  ;  Noyes  and  Ellis,  ibid.,  39,  2532  (1917)  ;  Lewis,  Brighton  and  Sebastian, 
ibid.,  39,  2245  (1917)  ;  Allmand  and  Polack,  J.  Chem.  Soc.  115,  1020  (1919)  ;  Randall 
and  Cushman,  J.  Am.  Chem.  Soc.  40,  393  (1918)  ;  Harned,  ibid.,  37,  2460  (1915)  ; 
Loomis,  Essex  and  Meacham,  ibid.,  39,  1133  (1917)  ;  Loomis  and  Acree,  Am.  Chem.  J.  46. 
632  (1911)  ;  Maclnnes  and  Beattie,  J.  Am.  Chem.  Soc.  42,  1117  (1920). 

»Tolman  and  Ferguson,  J.  Am.  Chem.  Soc.  34,  232  (1912). 


OTHER  PROPERTIES  OF  ELECTROLYTIC  SOLUTIONS  301 

cu 

that,  on  the  other  hand,  the  calculated  values  of  the  ratio  -~^  differ 


enormously  from  those  measured.    The  value  of  the  ratio  -^,  as  deter- 

Lu* 

mined  from  conductance  measurements,  may  be  somewhat  in  error 
owing  to  uncertainties  in  the  value  of  A0.  Since  the  value  of  1  —  y  is 
relatively  small,  it  is  obvious  that  a  small  error  in  the  value  of  A0 
will  have  a  large  effect  on  the  value  of  the  ratio  determined  from 
conductance  measurements.  Nevertheless,  it  is  evident  that  the  electro- 
motive force  as  measured  is  much  greater  than  that  calculated  according 
to  Equation  95. 

In  the  case  of  other  electrolytes  similar  results  have  been  obtained. 

C- 
In  the  following  table  are   given  values  of  -^  as  calculated  from  the 

°t2 

electromotive  force  of  potassium  chloride  concentration  cells.27  The 
concentrations  of  the  solutions  are  given  in  the  first  two  columns,  the 
values  found  and  calculated  for  the  ion  ratios  are  given  in  the  last  two 
columns. 

TABLE   CXXV, 

C  '• 
COMPARISON  OF  THE  RATIO  -^,  AS  DETERMINED  FROM  ELECTROMOTIVE 

% 
FORCE  AND  CONDUCTANCE  MEASUREMENTS. 

C  '  C- 


0.5  0.05  8.85  8.09 

0.1  0.01  9.16  8.33 

0.05  0.005  9.30  8.64 

0.01  0.001  9.62  9.04 

It  is  evident  that  the  ion  ratios  as  determined  by  means  of  conductance 
measurements  are  considerably  greater  than  those  calculated  from  the 
measured  electromotive  forces,  assuming  Equation  95  to  hold.  As  the 
solutions  become  more  dilute,  the  two  values  approach  each  other  slowly. 
The  explanation  of  these  phenomena  has  been  the  subject  of  much 
discussion.  The  observed  fact  is  that,  assuming  the  laws  of  dilute 
solutions  to  hold,  the  electromotive  force  of  a  concentration  cell  as 

"Maclnnes  and  Parker,  J.  Am.  Chem.  Soc.  S7,  1445  (1915). 


302        PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

measured  is  smaller  than  that  which  would  be  calculated  from  the  con- 
centrations of  the  ions  and  larger  than  that  calculated  from  the  con- 
centrations of  the  un-ionized  fraction.  One  obvious  explanation  is  that 
the  conditions  assumed  to  hold  in  applying  the  Nernst  equation  are 
not  fulfilled,  for  this  equation  obviously  can  apply  only  to  solutions 
which  are  sufficiently  dilute  so  that  the  deviations  from  ideal  systems 
lie  within  the  experimental  error.  The  behavior  of  solutions  of  strong 
electrolytes  clearly  shows  that  this  condition  is  not  fulfilled.  The 
Nernst  equation,  therefore,  should  not  apply. 

On  the  other  hand,  it  is  possible  that  the  ionization  measured  by 

means  of  the  conductance  ratio  -r-  is  not  correct.     If  this  is  true,  the 

A0 

concentrations  of  the  ions  are  not  known  and  it  is  therefore  not  possible 
to  calculate  the  electromotive  force  of  a  concentration  cell  from  Equa- 
tion 95.  In  this  case,  we  still  have  to  take  account  of  the  fact  that 
solutions  of  strong  electrolytes  do  not  fulfill  the  conditions  of  dilute 
solutions.  Consequently,  it  is  not  possible  to  calculate  from  the  electro- 
motive force  of  concentration  cells  the  concentrations  of  the  ions  in 
solution ;  for  it  may  readily  be  shown,  from  electromotive  force  measure- 
ments, that  the  law  of  mass  action  does  not  apply  to  solutions  of  strong 
electrolytes  and  that,  consequently,  the  laws  of  dilute  solution  do  not 
apply.  The  ratios  of  the  concentrations  of  the  ions,  therefore,  cannot 
be  calculated  by  means  of  the  Nernst  equation. 

It  has  been  suggested  that  strong  electrolytes  are  completely  ionized 
even  at  fairly  high  concentrations.  In  that  case  the  function  J 8  in 
Equation  96  measures  the  change  in  the  potential  of  the  electrolyte  due 
to  interaction  between  the  ions.  Granting  this  assumption,  the  function 
Js  has  a  negative  value  at  relatively  low  concentrations.  With  increas- 
ing concentration  the  value  of  J  diminishes,  passes  through  a  minimum, 
and  thereafter  increases,  passing  through  a  value  0  and  becoming  posi- 
tive at  very  high  concentrations.28 

A  considerable  number  of  measurements  have  been  made  on  the 
electromotive  force  of  concentration  cells  in  which  other  electrolytes  have 
been  added  to  the  solution  of  the  electrolyte  surrounding  one  electrode. 
Poma  and  Patroni 29  have  measured  the  electromotive  force  of  copper 
electrodes  in  solutions  of  copper  salts,  to  which  various  electrolytes 
with  a  common  ion  had  been  added.  Poma  30  measured  the  potential 
of  the  hydrogen  electrode  in  acid  solutions  in  the  presence  of  other  elec- 

28  The  manner  in  which  J  varies  is  discussed  further  in  the  next  chapter  as  is  also 
the  relation  of  this  function   to  the  activity. 

29  Poma  and  Patroni,  Ztschr.  f.  phys.  Chem.  87,  196    (1914). 
80Pojna,  Ztschr.  /.  phys.  Chem.  88,  671   (1914), 


OTHER  PROPERTIED  OF  ELECTROLYTIC  SOLUTIONS  303 

trolytes,  both  with  and  without  a  common  ion.  The  results  of  Poma 
indicate  a  considerable  change  in  the  electromotive  force  due  to  the 
addition  of  another  electrolyte.  The  effect  varies  with  the  concentra- 
tion and  also  with  the  nature  of  the  added  electrolyte.  At  the  higher 
concentrations  of  added  salt,  at  any  rate,  the  effect  is  greatly  dependent 
upon  the  nature  of  the  added  electrolyte,  the  electromotive  force  due  to 
the  addition  of  a  given  amount  of  electrolyte  being  the  greater  the 
greater  the  tendency  of  the  salt  to  form  hydrates.  The  sign  of  the 
electromotive  force,  moreover,  was  found  to  depend  upon  the  nature  of 
the  added  electrolyte. 

The  results  of  Poma  do  not  seem  to  be  in  good  agreement  with  the 
results  of  other  investigators  who  have  investigated  the  electromotive 
force  of  similar  cells.  The  potential  of  the  hydrogen  electrode  in  solu- 
tions of  hydrochloric  acid  in  the  presence  of  varying  amounts  of  alkali 
metal  chlorides  has  been  investigated  by  Chow,31  who  found  that,  keep- 
ing the  total  ion  concentration  constant,  the  potential  of  the  electrode 
in  the  mixture  may  be  calculated  according  to  Equation  95,  the  total 
concentration  of  hydrogen  and  of  chlorine  being  employed  for  the  con- 
centrations of  the  ions.  According  to  this  result,  the  function  J§  remains 

constant  in  the  mixture,  provided  the  total  concentration  of  the  mixed 
electrolytes  is  maintained  constant.  Similar  results  have  been  obtained 
by  Earned.32  The  results  of  Harned  indicate  that  at  low  concentra- 
tions the  function  Jl(!  has  the  same  value  for  the  mixture  as  it  has  for 

o 

the  pure  electrolyte  at  the  same  total  salt  concentration.  At  higher  con- 
centrations, according  to  Harned's  measurements,  the  potential  of  the 
electrolyte  depends  upon  the  nature  of  the  added  electrolyte.  It  was 
also  found  that  the  potential  of  the  hydrogen  electrode  in  hydrochloric 
acid  suffers  nearly  the  same  change  due  to  the  addition  of  equivalent 
amounts  of  potassium  chloride  and  sodium  bromide. 

As  yet,  experimental  data  in  this  direction  are  not  sufficiently  exten- 
sive to  warrant  generalizing  the  conclusions  drawn  from  the  investiga- 
tions referred  to  above. 

6.  Thermal  Properties  of  Electrolytic  Solutions.  It  is  only  recently 
that  the  technique  of  thermal  measurements  has  been  refined  to  a  point 
where  data  obtained  with  electrolytic  solutions  are  sufficiently  precise 
to  make  an  inter-comparison  of  the  various  thermal  properties  of  such 
solutions  generally  possible.  Even  now,  accurate  data  are  available  for 
only  a  limited  number  of  systems,  as  a  result  of  which  but  few  general 

"Chow,  J.  Am.  Chem.  Soc.  &,  497  (1920). 

"Earned,  J.  Am.  Chem.  SQC.  42,  1808  (1920)  ;  i&itf,,  37,  2460  U9J5), 


304        PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

conclusions  may  at  the  present  time  be  reached  relative  to  the  manner 
in  which  the  thermal  quantities  are  dependent  upon  the  various  factors 
governing  the  condition  of  a  solution. 

Water,  itself,  is  ionized,  and  the  energy  of  the  ionization  reaction 
corresponds  very  satisfactorily  with  the  heats  of  neutralization  of  strong 
acids  and  bases.  According  to  the  Ionic  Theory,  the  heats  of  neutraliza- 
tion of  different  strong  acids  and  bases  should  be  the  same  at  low  con- 
centrations, since  the  neutralization  process  under  these  conditions  con- 
sists essentially  in  a  combination  of  the  hydrogen  and  hydroxyl  ions  to 
form  water.  The  most  reliable  determination  of  the  heats  of  neutraliza- 
tion was  made  by  Wormann.33  The  mean  value  of  the  heat  of  neu- 
tralization for  hydrochloric  and  nitric  acids  with  sodium  and  potassium 
hydroxides  at  18°  was  found  to  be  approximately  13700  calories.  The 
heat  of  ionization  of  water  is  related  to  the  ionization  constant  of  water 
by  means  of  the  equation: 

(97)  d\ogK_      U 

dT        ~  RT2' 

where  U  is  the  energy  change  accompanying  the  ionization  of  one  mol 
of  water.  Noyes  and  his  associates 3*  have  measured  the  ionization 
constant  of  water  at  a  series  of  temperatures  up  to  218°.  The  heat  of 
ionization  derived  from  their  results  is  in  good  agreement  with  the  value 
found  by  Wormann  for  the  heat  of  neutralization.  Thus  at  18°  Noyes 
finds  that  the  value  14055  is  in  agreement  with  his  experimental  values. 
Direct  determinations  of  the  heat  of  neutralization  of  strong  acids  and 
bases  at  higher  temperatures  do  not  appear  to  exist,  so  that  a  compari- 
son in  these  regions  cannot  be  made.  At  higher  temperatures  the  ioniza- 
tion constant  of  water  passes  through  a  maximum,  as  a  consequence  of 
which  it  follows  that  the  heat  of  ionization  changes  sign. 

Equation  97  is  likewise  applicable  to  the  ionization  process  of  elec- 
trolytes in  water.  If  the  ionization  values  are  known  at  different  tem- 
peratures, the  energy  change  accompanying  the  ionization  process  may 
be  calculated,  assuming  that  the  energy  change  accompanying  the  process 
remains  constant.  The  equation  holds  true  even  though  the  conditions 
for  dilute  systems  are  not  fulfilled,  provided  the  concentrations  enter- 
ing in  the  equation  represent  the  real  concentrations  of  the  molecular 
species  in  question.  Thermal  data  of  sufficient  precision  are  not  avail- 
able to  make  it  possible  to  determine  to  what  extent  the  results  of  con- 
ductance measurements  at  different  temperatures  are  in  agreement  with 
thermal  data.  In  a  general  way,  however,  the  results  appear  to  be  in 
agreement.  In  the  case  of  the  weak  acids  and  bases,  the  order  of 

*  Wormann,  Ann.  D.  Phys.  18,  775   (1905). 
•«  Carnegie  Publications,  No.  63   (1907). 


OTHER  PROPERTIES  OF  ELECTROLYTIC  SOLUTIONS  305 

magnitude  of  the  energy  effects,  as  derived  from  conductance-temperature 
measurements,  agrees  with  those  derived  from  the  heats  of  dilution  of 
solutions  of  weak  electrolytes.  The  ionization  constants  of  acetic  acid 
and  ammonia,  for  example,  have  maxima  in  the  neighborhood  of  ordi- 
nary temperatures,  indicating  that  the  energy  change  accompanying  the 
ionization  process  is  zero;  correspondingly,  the  heats  of  dilution  of 
solutions  of  these  substances  have  small,  although  uncertain,  values.  In 
general,  weak  electrolytes  have  a  greater  heat  of  dilution  than  strong 
electrolytes  and,  correspondingly,  their  ionization  changes  more  largely 
with  temperature. 

The  heats  of  dilution  of  strong  electrolytes  unquestionably  have 
very  small  values.  Correspondingly,  the  ionization  of  strong  electrolytes 
at  ordinary  temperatures  changes  but  little  with  temperature.  The 
ionization  of  certain  salts,  such  as  magnesium  sulphate,  decreases 
markedly  at  higher  temperatures;  and  it  is  to  be  expected  that  solutions 
of  these  salts  will  exhibit  an  appreciable  heat  of  dilution  even  at  rela- 
tively low  concentrations.  Experimental  determinations  of  these  quan- 
tities, however,  are  lacking.  In  view  of  the  uncertainty  of  the  thermal 
data,  it  cannot  be  stated  that  the  commonly  accepted  ionic  theory  leads 
to  results  which  are  in  contradiction  with  the  thermal  properties  of 
electrolytic  solutions. 

Recently,  careful  determinations  of  the  heats  of  dilution  of  a  number 
of  electrolytes  have  been  made  by  a  number  of  investigators.  Accord- 
ing to  Randall  and  Bisson,35  the  heat  of  dilution  of  sodium  chloride  from 
0.28  N  to  zero  concentration  amounts  to  only  two  calories.  At  higher 
concentrations  the  heat  of  dilution,  although  small,  is  quite  marked. 
The  heats  of  dilution  of  a  number  of  salts,  as  well  as  of  mixtures  of 
salts,  have  been  determined  by  Stearn  and  Smith,36  and  Smith,  Stearn 
and  Schneider.37  The  heats  of  dilution  for  sodium  and  potassium 
chlorides  were  found  to  be  very  nearly  the  same,  although  varying 
slightly  at  high  concentrations.  At  low  concentrations,  the  heat  of  dilu- 
tion, in  all  cases,  approaches  a  value  of  zero,  as  might  be  expected.  The 
heats  of  dilution  are  not  in  all  cases  of  the  same  sign,  since  that  of 
strontium  chloride  is  opposite  in  sign  from  that  of  sodium  and  potassium 
chlorides.  The  heats  of  dilution  for  mixtures  of  two  electrolytes  in 
general  differs  markedly  from  the  mean  heat  of  dilution  of  the  con- 
stituents. Stearn  and  Smith  suggest  that  this  result  may  be  due  to  the 
fact  that  complex  compounds,  whose  formation  presumably  would  be 
accompanied  by  an  energy  change,  are  formed  in  mixtures  of  salts.  For 
sodium  and  potassium  chlorides  the  heat  of  dilution  is  negative,  which 

»8  Randall  and  Bisson,  J.  Am.  Chem.  S<tc.  42,  347   (1920). 
86  Stearn  and  Smith,  J.  Am.   Chem.  Soc.  1&,  18   (1920). 
"  Smith,  Stearn  and  Schneider,  ibid.,  #,  3$  (1920). 


306        PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

corresponds  to  an  increase  in  the  ionization  of  these  electrolytes  with  the 
temperature.  This  is  not  in  agreement  with  the  observed  results  of 
conductance  measurements.  It  is  possible,  however,  that  the  energy 
change  measured  on  the  dilution  of  a  solution  includes  effects  other  than 
those  due  to  change  in  the  ionization  of  the  electrolyte.  Certainly,  at 
the  higher  concentrations,  it  is  to  be  expected  that  a  change  in  the 
hydration  of  the  ions,  and  possibly  of  the  neutral  molecules,  takes  place, 
and  the  energy  change  accompanying  these  processes  may  obscure  the 
energy  change  due  to  the  ionization  process. 

It  appears,  thus,  that  a  knowledge  of  the  thermal  properties  of  elec- 
trolytic solutions  has  a  very  direct  bearing  on  our  interpretation  of  the 
phenomena  observed  in  electrolytic  solutions.  In  order  to  analyze  the 
more  or  less  complex  processes  into  their  constituent  effects,  however, 
further  experimental  data  are  required. 

In  this  connection,  it  should  also  be  noted  that  a  number  of  investi- 
gators,38 from  a  study  of  the  temperature  coefficient  of  the  electromotive 
force  of  concentration  cells,  have  obtained  values  for  the  energy  changes 
accompanying  the  transfer  of  electrolytes  from  solutions  of  one  concen- 
tration to  another.  Harned  has  also  determined  the  energy  changes 
accompanying  the  transfer  of  hydrochloric  acid  from  a  solution  con- 
taining a  mixture  of  salt  and  acid  to  one  containing  acid  alone.  Hydro- 
chloric acid  and  chlorides  were  employed  in  these  mixtures. 

In  the  following  table  are  given  values  of  the  energy  change  accom- 
panying the  transfer  of  one  mol  of  electrolyte  from  the  concentration 
given  to  a  concentration  of  0.1  N,  according  to  Ellis  and  Harned. 

TABLE  CXXVI. 

ENERGY  CHANGE,  IN  JOULES,  ACCOMPANYING  THE  TRANSFER  OF  ONE 
MOL  OF  ELECTROLYTE  FROM  A  CONCENTRATION  C  TO  A  CON- 
CENTRATION 0.1  N  AT  25°. 

C  KC1  NaCl  HC1 

0.1000  000  000  000 

0.3000  —355  —300  420 

0.5000  —650  —570  820 

1.000  —1310  —1196  1820 

1.500  —1900  —1780  2770 

2.000  —2375  —2300  3720 

2.500  —2810  —2690  4740 

3.000  —3175  —3010  5710 

As  may  be  seen  from  the  table,  the  energy  changes  accompanying  the 
transfer  of  sodium  and  potassium  chlorides  differ  but  little.  The  sign  of 

"Ellis,  J.  Am.  CUem.  Soc.  38,  737   (1916)  ;  Harned,  ibid.,  #t  1808   (1920). 


OTHER  PROPERTIES  OF  ELECTROLYTIC  SOLUTIONS  307 

the  energy  change  in  the  case  of  hydrochloric  acid  is  opposite  from  that 
of  sodium  and  potassium  chlorides. 

Earned  has  also  determined  the  energy  changes  accompanying  the 
transfer  of  hydrochloric  acid  from  solutions  containing  hydrochloric  acid 
of  concentration  0.1  N,  together  with  an  added  salt  having  a  common 
chloride  ion  at  varying  concentrations,  C,  to  a  solution  of  pure  hydro- 
chloric acid  at  a  concentration  of  0.1  N.  The  results  are  given  in  the 
following  table. 

TABLE  CXXVII. 

ENERGY  CHANGE  ACCOMPANYING  THE  TRANSFER  OF  Two  MOLS  OF  HC1  FROM  SOLUTIONS 
OF  0.1  N  HC1  +  CN  MCI  TO  A  SOLUTION  OF  0.1  N  HC1  AT  25°. 

KC1 

C   05018  0.5086  1.0346  2.134  3.309 

AH  6  37  149  1371  2807 

NaCl 

C  0.1003  0.2014  0.5061  0.9183  1.023  1.871  2.094  2.711  3.202  3.726 

AH  —44   142    273    569   755   2373  2381  3595  4647  5942 

LiCl 

C   0.8485  1.7267  2.636  3.574  4.556 

A#    1407  4128  6527  9200  11610 

It  will  be  observed  that  the  energy  change  is  greatest  for  LiCl  and 
least  for  KC1.  Apparently,  the  energy  change  is  greatest  for  those  salts 
which  exhibit  the  greatest  tendency  to  form  hydrates.  These  energy 
changes  persist  below  0.1  N.  This  is  apparently  also  the  case  in  solu- 
tions of  the  pure  electrolytes.39 

7.  Change  of  the  Transference  Numbers  at  Low  Concentrations. 
The  transference  numbers  of  an  electrolyte  are  determined  by  the  rela- 
tive speed  of  its  ions.  Any  influence,  therefore,  which  tends  to  alter  the 
relative  speed  of  the  ions  obviously  tends  to  alter  the  transference  num- 
bers of  the  electrolyte.  The  speed  of  the  ions  is  a  function  of  the  vis- 
cosity of  the  solution  and,  for  a  given  change  of  viscosity,  the  change  in 
the  speed  of  an  ion  depends  upon  the  nature  of  the  ion.  This,  for 
example,  is  evident  from  the  effect  of  temperature  on  the  ionic  conduc- 
tances, where,  as  we  have  seen,  the  temperature  effect  is  the  smaller  the 
greater  the  conductance  of  the  ion.  At  higher  concentrations,  therefore, 
where  the  viscosity  effect  is  appreciable,  a  change  in  the  value  of  the 
transference  numbers  is  not  unexpected.39*  At  low  concentrations,  how- 
ever, we  should  expect  the  transference  numbers  to  be  constant. 

This  condition  is  apparently  not  fulfilled  in  solutions  of  strong  acids 
and  bases.  For  example,  the  anion  transference  number  of  hydrochloric 

39  Compare  Ellis,  loc.  cit. 

3»"  It  has  been  found  that  the  transference  number  of  lithium  chloride  is  not  altered 
on  the  addition  of  raffinose  (Millard,  Thesis,  Univ.  of  111.  (1914)).  Reference  to  Table 


308        PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

acid  in  water  at  18°  varies  from  0.168  at  0.005  N  to  0.165  at  0.1  N.40 
In  a  sense,  this  does  not  appear  to  be  a  great  change  in  the  value  of  the 
transference  number.  Nevertheless,  it  is  in  excess  of  what  might  be 
expected  from  the  viscosity  effect  in  these  solutions.  Furthermore,  the 
conductance  of  the  chloride  ion  as  calculated  from  the  transference 
number  and  the  degree  of  ionization  does  not  correspond  with  the  value 
of  the  conductance  of  the  chloride  ion  at  infinite  dilution  in  solutions  of 
potassium  chloride.  Assuming  for  the  transference  number  of  the 
chloride  ion  in  hydrochloric  acid  the  value  0.167  and  for  the  ionization 
the  value  0.972  and  for  the  conductance  the  value  369.3  at  0.01  N  and 
18°,  we  obtain,  for  the  conductance  of  the  chloride  ion,  the  value 

x  167 


—        Q7Q        =  62.68.     At  infinite  dilution  the  con- 

ductance of  the  chloride  ion  has  a  value  of  65.5.  It  appears,  then, 
that  up  to  a  concentration  of  0.01  N  the  conductance  of  the  chloride  ion 
has  fallen  from  a  value  of  65.5  to  a  value  of  62.68.  This  value  is  obvi- 
ously subject  to  a  correction,  since,  in  calculating  the  -value  of  y  by  the 

ratio—  r-,  it  has  been  tacitly  assumed  that  the  speed  of  the  ions  remains 
A0 

constant. 

Noyes  41  called  attention  to  this  discrepancy  which  exists  in  the  case 
of  the  strong  acids.  Lewis42  showed  that  the  ionization  of  different 
chlorides  as  calculated  from  the  conductance  of  the  chloride  ion  at  a 
given  concentration  is  the  same  for  all  chlorides.  Maclnnes  43  has  inves- 
tigated the  conductance  of  various  ions  at  higher  concentrations  in  some 
detail.  The  conductance  of  an  ion  at  a  given  concentration  is  obtained 
by  multiplying  the  conductance  of  the  electrolyte  by  the  transference 
number  of  the  ion  in  question  at  that  concentration.  In  the  case  of  the 
chlorides,  he  obtained  the  following  results: 

XLIII  will  show  that  the  conductance  of  lithium,  caesium  and  potassium  chlorides  Is 
affected  to  almost  the  same  extent  on  the  addition  of  raffinose.  Evidently,  the  viscosity 
change  due  to  raffinose  affects  the  L.i+,  Cs+  and  K+  ions  to  the  same  extent.  From  the 
game  table,  it  is  evident  that  the  conductance  of  potassium  chloride  and  lithium  chloride 
is  altered  to  very  nearly  the  same  extent,  even  on  the  addition  of  some  non-electrolyte  of 
relatively  low  molecular  weight.  In  methyl  alcohol,  however,  the  exponent  p  is  markedly 
larger  for  LiCl  than  for  CsCl.  In  the  presence  of  this  non-electrolyte,  the  influence  of 
viscosity  on  ion  conductance  depends  upon  the  nature  of  the  ion.  Correspondingly,  Mil- 
lard  (loc.  cit.)  found  that  the  transference  number  of  the  lithium  ion  in  lithium  chloride 
solution  is  decreased  from  0.322  to  0.307  on  the  addition  of  0.4  mol  of  methyl  alcohol 
per  1000  g.  of  water.  The  viscosity  effect  due  to  the  electrolyte  itself  has  an  influence 
on  the  conductance  of  an  ion  which  differs  markedly  from  that  due  to  a  non-electrolyte 
of  large  molecular  weight.  In  considering  the  influence  of  viscosity  on  the  speed  of  an 
ion,  the  nature  of  the  particles  to  which  the  viscosity  change  is  due  must  not  be  lost 
sight  of. 

«  Noyes  and  Kato,  J.  Am.  Chem.  Soc.  30,  318  (1908). 

"Noyes  and  Sammet,  J.  Am.  Chem.  Soc.  24,  944  (1902)  ;  ibid..  25.  165  (1903)  :  Ztschr 
f.  phya.  Cfhem.  43,  49  (1903)  ;  Noyes  and  Kato,  ibid.,  62,  420  (1908). 

"Lewis,  J.  Am.  Chem.  Soc.  3Jf,  1631    (1912). 

"Maclnnes,  J.  Am.  Chem.  Soc.  41,  1086  (1919)  ;  ibid.,  43f  1217  (1921). 


OTHER  PROPERTIES  OF  ELECTROLYTIC  SOLUTIONS  309 

TABLE   CXXVIII. 

CONDUCTANCE  OF  THE  CHLORIDE  ION  AT  18°  AS  DERIVED  FROM  THE  CON- 
DUCTANCE AND  THE  TRANSFERENCE  NUMBERS  OF  DIFFERENT 
ELECTROLYTES  AT  0.01  N  AND  18°. 

A  n  TC1          TclArr 

HC1 369.3  1.0005  0.167  61.67 

CsCl    125.07  0.9997  0.495  61.89 

KC1    122.37  0.9996  0.504  61.68 

NaCl 101.88  1.0009  0.604  61.55 

LiCl' 91.97  1.0016  0.668  61.48 

Here  TTQJ  is  the  transference  number  of  the  chloride  ion  and  T^Ari0-7 

is  the  conductance  of  the  chloride  ion  corrected  for  viscosity.  From  an 
inspection  of  this  table,  it  is  evident  that  the  conductance  of  the  chloride 
ion,  as  derived  from  the  transference  numbers  and  conductances  of  dif- 
ferent chlorides,  is  the  same.  The  ion  conductances  given  in  the  last 
column  have  been  corrected  for  the  viscosity  according  to  Equation  41, 
assuming  for  the  exponent  p  the  value  0.7.  This  viscosity  correction  is 
uncertain,  but  in  view  of  the  fact  that  the  viscosity  effect  in  all  these 
solutions  is  scarcely  in  excess  of  0.1  per  cent  it  is  evident  that  the  vis- 
cosity correction  can  have  only  a  minor  influence.  While  the  conduc- 
tance of  the  chloride  ion  in  the  different  chlorides  is  very  nearly  the 
same,  it  does  not  appear  to  be  identical.  In  lithium  chloride,  for  ex- 
ample, the  conductance  is  approximately  0.7  per  cent  lower  than  it  is 
in  caesium  chloride,  and  from  caesium  chloride  to  lithium  chloride  the 
conductances  vary  in  the  order:  caesium,  potassium,  sodium,  lithium. 
If  the  differences  were  purely  accidental,  we  should  not  expect  any  such 
regularity  in  the  order  of  the  conductance  values.  Maclnnes  has  also 
made  a  similar  comparison  at  higher  concentrations  up  to  and  including 
1.0  N.  Throughout  he  obtains  excellent  agreement  among  the  conduc- 
tance values  of  the  chloride  ion  in  different  chlorides.  It  should  be 
noted,  however,  that,  at  the  higher  concentrations,  the  viscosity  effects 
are  considerable,  and  the  ion  conductances  in  consequence  are  propor- 
tionately in  doubt. 

Maclnnes  is  inclined  to  believe  that  it  is  generally  true  that  at  a 
given  concentration  the  conductance  due  to  a  given  ion  is  independent 
of  the  nature  of  other  ions  present  in  the  solution.  This  generalization, 
however,  does  not  appear  to  be  wholly  justified.  For  example,  assuming 
the  transference  values  given  by  Noyes  and  Falk,  we  obtain  for  the 
conductance  of  the  nitrate  ion  at  0.2  N  in  solutions  of  KN03,  AgN03 


310        PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

and  HN03  the  values  57.28,  55.60  and  56.40  respectively.  There  is, 
however,  a  considerable  degree  of  uncertainty  attached  to  these  calcu- 
lations owing  to  uncertainties  in  the  values  of  the  transference  numbers. 
The  errors  with  which  transference  measurements  are  affected  are  rela- 
tively large  and  it  is  possible  that  consistent  errors  are  present,  in  which 
case  the  probable  error  of  the  determination  cannot  be  estimated  from 
the  consistency  of  a  given  series  of  measurements.  In  many  respects,  it 
would  appear  that  transference  measurements  by  the  moving  boundary 
method  should  be  more  nearly  comparable  than  those  by  other  methods. 
In  Table  CXXIX  are  given  values  of  the  ion  conductance  Aj^+  of  the 

A£+ 

potassium  ion  and  of  •  for  the   same   ion   for   different  potassium 

salts  at  concentrations  of  0.02  N  and  0.1  N.  The  ionization  and  con- 
ductance values  are  taken  from  Noyes  and  Falk  and  the  transference 
values  from  Dennison  and  Steele.4*  The  numbers  in  the  next  to  the  last 
column  are  the  ion  conductances,  which  should  have  the  same  value  if 
the  conductance  of  a  given  ion  at  a  given  concentration  were  independent 
of  the  nature  of  the  other  ion  with  which  it  is  combined.  In  the  last 


column  are  given  the  values  of 


which,  if  the  transference  num- 


ber is  independent  of  concentration  and  the  ionization  is  measured  by 
the  ratio  -r-,  should  correspond  with  the  conductance  of  the  potassium 

A0 

ion  at  infinite  dilution. 


T 
VALUES  OF  A^+  AND  OF 

TC 
KC1   0.493 

ABLE    CXX 
A£+ 

IX. 

FERENT  POTASSIUM 

Ac            Ax+ 

119.9           59.13 
115.0           57.78 
121.7            58.68 
108.8           58.12 
102.0            57.84 
120.9            58.90 

i  SALTS. 
AK+ 

Y 
At  0.02  N. 

Y 

0.922 
0.911 
0.921 
0.910 
0.910 
0.922 

Y 
64.14 
63.44 
63.72 
63.88 
63.58 
63.90 

KNOQ 

....     0  502 

KBr   

0  482 

KC1CX 

0.534 

KBr03  

0  567 

KI  

0.487 

Mean 
A.D. 

58.41 
0.50 

Mean  63.78 
A.D.     0.20 

**  Dennison  and  Steele,  Phil.  Trans.  A,  205,  462   (1906). 


OTHER  PROPERTIES  OF  ELECTROLYTIC  SOLUTIONS 

TABLE  CXXIX.— Continued 
At  0.1  N. 

A«  v..  A  A  rr+ 


KC1  . 
KN03 
KBr  . 


130.0 

126.3 

. .  132.2 

KC103    119.6 

KBrO3  112.1 

KI  .  131.1 


0.861 

111.97 

55.10 

0.829 

104.71 

52.60 

0.863 

114.14 

54.92 

0.829 

99.14 

53.17 

0.829 

93.0 

52.98 

0.870 

113.98 

55.40 

311 


AX* 
Y 

64.04 
63.50 
63.64 
64.14 
63.93 
63.68 


Mean  54.03    Mean  63.82 
A.D.      1.11     A.D.     0.21 

It  will  be  observed  that  at  0.02  N  the  value  of  \K+  varies  from  57.78 

Ai^+ 


to  59.13  with  a  mean  deviation  of  0.50,  while 


varies  from  63.44 


to  64.14  with  a  mean  deviation  of  0.20.    At  a  concentration  of  0.1  N 
the  value  of  A^+  varies  from  52.60  to  55.40  with  a  mean  deviation  of 

^K+ 
1.11.  while  the  value  of  varies  from  63.50  to  64.14  with  a  mean 

7 
deviation  of  0.21.    It  is  evident  that  the  conductance  of  the  potassium 


ion  in  different  salts  is  not  the  same,  while  the  ratio 


is  substan- 


tially the  same.45  These  results,  therefore,  do  not  bear  out  the  conclu- 
sion that  the  conductance  of  an  ion  is  independent  of  the  other  ion  with 
which  it  is  combined.  Leaving  aside  for  the  moment  the  strong  acids 
and  bases,  it  appears  that  conductance  and  transference  measurements 
agree  with  the  assumption  that  the  conductance  of  a  given  ion  varies 
with  the  nature  of  its  co-ion  and  that  the  difference  in  the  conduction 
of  a  given  ion  is  proportional  to  the  ionization  of  its  salt.  The  reason 
why  the  conductance  of  the  chloride  ion  is  found  the  same  for  different 
electrolytes  is  due  to  the  fact  that  the  ionization  of  these  electrolytes  is 
the  same  at  the  same  concentration.  If  corrected  values  of  the  con- 
ductance are  employed,  the  ionization  of  sodium,  potassium,  and  lithium 
chlorides,  as  determined  from  conductance  measurements,  is  substan- 
tially the  same  up  to  1.0  N.  Up  to  a  concentration  where  the  viscosity 
effects  begin  to  become  appreciable  there  is  no  certain  evidence  indicat- 
ing that  the  relative  speeds  of  the  ions  undergo  change.  In  the  case  of 

45  This   conclusion    was   reached    by   Dennison    and    Steele    (Phil.    Trans.   A    205,   462 
(1906) ). 


312        PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

the  strong  acids  and  bases,  however,  the  experimental  data  indicate  that 
the  speed  of  one  of  the  ions,  at  least,  undergoes  a  marked  change  at 
concentrations  below  10~2  N.  The  nature  of  the  process  to  which  this 
change  is  due  remains  uncertain. 

8.  Reactions  in  Electrolytic  Solutions.  Electrolytic  solutions,  in 
water  at  least,  are  characterized  by  the  speed  with  which  they  take  place, 
as  well  as  by  their  reversibility.  This  property  of  electrolytic  solutions 
has  been  cited  in  support  of  the  ionic  theory;  and,  indeed,  the  reactions 
among  electrolytes  clearly  indicate  some  common  condition  as  a  result 
of  which  they  take  place  with  great  facility  and,  as  a  rule,  with  the 
accompaniment  of  a  comparatively  small  energy  change.  It  is  only  in 
a  few  other  systems  that  reactions  similarly  take  place  with  great  speed, 
and  many  of  these  are  irreversible.  Reactions  in  fused  salts  and  in  the 
metals,  however,  resemble  those  in  electrolytic  solutions  in  many  re- 
spects. There  is  little  question  but  that  reactions  in  fused  salts  are  ionic 
in  character.  While  available  data  are  extremely  meager  in  the  case 
of  the  metals,  there  is  evidence  which  indicates  that  here,  too,  reactions 
may  be  ionic. 

In  a  few  instances,  in  water  as  well  as  in  some  other  solvents,  solu- 
tions of  electrolytes  do  not  reach  equilibrium  at  once  when  an  elec- 
trolyte is  dissolved.  In  those  cases  which  have  been  studied  in  detail, 
it  has  been  shown  that  intermediate  reactions  occur  which  greatly  influ- 
ence the  properties  of  the  solution;  so,  for  example,  certain  of  the  metal- 
ammonia  salts,  when  first  dissolved  in  water,  yield  solutions  which  are 
very  poor  conductors  of  the  current,  but  which,  on  standing,  show  a 
marked  increase  in  conductance.  Here,  unquestionably,  the  gradual 
increase  of  the  conductance  is  due  to  a  reaction  as  a  result  of  which  the 
metal-ammonia  complex  is  affected.  The  original  complex  is  not  capable 
of  ionization,  while  the  resulting  product  is  ionized.  These  particular 
reactions  are  accounted  for  by  Werner's  theory.  Aside  from  a  few  cases 
of  this  type,  solutions  of  electrolytes  reach  a  condition  of  equilibrium 
as  soon  as  the  process  of  solution  is  completed. 

It  will  be  unnecessary,  here,  to  discuss  reactions  in  aqueous  solutions 
since  these  are  familiar  to  everyone  who  has  studied  the  elements  of 
chemistry.  Since  solutions  in  non-aqueous  solvents  are  ionized,  we  may 
expect  that  similar  reactions  take  place  in  solutions  in  these  solvents. 
The  nature  of  the  reactions  will,  of  course,  depend  upon  the  nature  of 
the  solvent  as  well  as  upon  that  of  the  dissolved  electrolytes. 

The  multiplicity  of  electrolytic  reactions  in  aqueous  solvents  is  in 
part  due  to  the  electrolytic  properties  of  water  itself.  As  we  have  seen, 
water  is  ionized  to  a  slight  extent  into  hydrogen  and  the  hydroxyl  ions. 


OTHER  PROPERTIES  OF  ELECTROLYTIC  SOLUTIONS  313 

When  one  or  more  electrolytes  are  dissolved  in  water,  the  resulting  reac- 
tion is  influenced  by  the  presence  of  these  ions  -due  to  the  solvent.  We 
should  expect  similar  reactions  in  the  case  of  all  solvents  capable  of 
ionization.  This  includes,  in  the  first  place,  solvents  containing  hydro- 
gen, such  as  the  liquid  halogen  acids,  ammonia,  hydrocyanic  acid,  formic 
acid,  acetic  acid,  the  alcohols,  the  amines,  etc.  In  all  these  cases,  it  is 
to  be  anticipated  that  the  solvent  will  furnish  a  positive  hydrogen  ion 
and  a  negative  ion  corresponding  to  the  constitution  of  the  solvent.  The 
hydrogen  or  acid  ion  of  substances  dissolved  in  solvents  which  them- 
selves yield  a  hydrogen  ion  will  exhibit  acid  properties.  The  negative 
ion,  correspondingly,  may  be  considered  as  a  basic  ion  and  salts  of  this 
ion  will  act  as  bases  when  dissolved  in  a  solvent  yielding  the  same  ion. 
So,  in  the  case  of  the  alcohols,  the  acids  exhibit  acidic  properties,  while 
the  alcoholates  exhibit  basic  properties.  Similarly,  in  ammonia,  the 
ammonium  salts  exhibit  acidic  properties,  while  the  basic  amides  exhibit 
basic  properties.  On  the  other  hand,  a  base  typical  of  water,  such  as 
tetramethylammonium  hydroxide,  would  properly  be  classed  as  a  salt 
when  dissolved  in  ammonia.  However,  many  of  the  characteristic  prop- 
erties of  acids  and  bases  are  not  entirely  dependent  upon  the  presence 
of  a  positive  or  a  negative  ion  in  common  with  the  solvent.  For  example, 
any  salt  of  a  strong  base  and  a  weak  acid  will  exhibit  properties. charac- 
teristic of  a  base  when  in  solution.  Thus,  tetramethylammonium  hydrox- 
ide in  ammonia  exhibits  basic  properties,  very  similar  to  those  of  potas- 
sium amide,  the  reason  for  which  lies  in  the  fact  that  the  resulting  acid 
formed  by  the  hydrolysis,  or  ammonolysis,  of  this  salt  in  ammonia  is  a 
very  weak  acid  water,  which,  as  we  know,  is  only  very  slightly  ionized 
in  liquid  ammonia.  Correspondingly,  a  cyanide  dissolved  in  water 
exhibits  basic  properties  for  the  reason  that  hydrocyanic  acid  is  only 
slightly  ionized  in  water.  Strictly  speaking,  an  acid  has  a  positive  ion 
and  a  base  a  negative  ion  in  common  with  the  solvent;  nevertheless, 
salts  of  strong  acids  and  very  weak  bases  and  salts  of  strong  bases  and 
very  weak  acids  exhibit  certain  acidic  and  basic  properties  in  solution. 
We  have  seen  that  the  OH~  ion  is  a  characteristic  basic  ion  only  in 
aqueous  solution  and  that  in  other  solvents  other  ions  function  as  basic 
ions.  So,  also,  any  positive  ion  common  to  a  solvent  will  in  that  solvent 
exhibit  many  of  the  properties  of  an  acid  ion.  For  example,  iron  intro- 
duced into  an  aqueous  solution  of  an  acid  yields  a  salt  and  hydrogen. 
Similarly,  iron  introduced  into  molten  lead  salt  yields  a  corresponding 
salt  of  iron  and  metallic  lead.  Excepting  for  the  fact  that  in  the  first 
case  hydrogen  is  a  gas  and  in  the  second  case  lead  is  a  liquid  metal, 
there  is  no  essential  distinction  in  the  nature  of  the  reaction  in  the  two 


314        PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

cases.  The  number  of  examples  of  this  type  might  be  greatly  multiplied. 
Liquid  ammonia  is  the  only  non-aqueous  solvent  in  which  electrolytic 
reactions  have  been  extensively  studied  so  that  this  discussion  must  be 
largely  confined  to  solutions  in  this  solvent.  The  study  of  reactions  in 
ammonia  have  led  to  a  considerable  extension  of  our  notions  respecting 
electrolytic  reactions  in  general,  and  have  greatly  advanced  our  knowl- 
edge regarding  the  nature  of  various  nitrogen  compounds.  Solutions  in 
ammonia  exhibit  properties  similar  to  those  of  solutions  in  water,  be- 
cause of  the  similarity  of  constitution  of  the  two  solvents.  In  water  we 
have  the  ionization  reaction: 

H20  =  H+  +  OH- 

and  in  ammonia  the  corresponding  reaction: 

NH3  =  H+  +  NH2-. 

The  negative  ions  in  ammonia  and  water  differ,  but  exhibit  many  points 
of  similarity.  The  positive  ions  in  the  two  solvents  are  the  same  and 
exhibit  a  similar  behavior.  In  ammonia  solutions,  however,  the  hydrogen 
ion  appears  to  be  identical  with  the  ammonium  ion,  whereas  in  aqueous 
solution  the  hydrogen  ion  is  in  all  likelihood  a  complex  between  hydro- 
gen and  water,  so  that  the  two  ions  are  not  identical.  The  same  is  doubt- 
less true  of  most  ions.  In  their  essential  behavior,  however,  the  hydrogen 
ions  in  ammonia  do  not  differ  materially  from  the  hydrogen  ions  in 
water.  One  of  the  characteristic  properties  of  the  hydrogen  ions  is  its 
tendency  to  react  with  metals  to  form  a  salt  and  hydrogen.  In  water, 
for  example,  we  have  the  reaction: 

Mg  +  2HC1  =  MgCl2  +  H2. 
So,  in  ammonia  we  have  the  reaction: 

Mg  +  2NH.C1  =  MgCl2  +  H2  +  2NH3. 

In  this  last  reaction,  the  ammonia  resulting  from  the  reaction  is  identical 
with  the  solvent  molecules  and  therefore  may  be  omitted  from  the  reac- 
tion equations.  In  aqueous  solutions  of  the  acids  this  is  always  done, 
for  it  is  less  evident  that  water  is  concerned  in  the  reaction.  In  am- 
monia, the  acids  react  with  bases  to  form  salts  and  water,  corresponding 
to  the  reactions  in  aqueous  solutions;  thus: 

(CH3)4NOH  +  HC1  =  (CH3)4NC1  +  H2O  in  water, 
and  (CH3)4NOH  +  NH4C1=  (CH3)4NC1  +  NH3  +  H20  in  ammonia. 


OTHER  PROPERTIES  OF  ELECTROLYTIC  SOLUTIONS  315 

In  aqueous  solutions,  with  a  few  exceptions,  the  acids  are  substances 
in  which  the  hydrogen  is  joined  to  an  electronegative  group  through  an 
oxygen  atom.  For  example,  in  the  case  of  acetic  acid  we  have 
CH3COO-H+.  Such  acids  are  known  as  hydroxy-acids,  or  perhaps 
better  aquo-acids,  as  Franklin  has  suggested.  Similarly,  in  the  case  of 
ammonia,  substances  in  which  the  hydrogen  atoms  are  connected  to  an 
electronegative  group  through  the  intermediary  of  a  nitrogen  atom  are 
acids.  This  is  a  class  of  substances  commonly  known  as  the  acid  amides 
or  imides.  Thus,  we  have,  corresponding  to  acetic  acid  CH3COOH, 
acetamide  CH3CONH2.  Acetamide  is  therefore  an  acid  related  to  am- 
monia as  acetic  acid  is  to  water,  and,  according  to  Franklin,  may  be 
called  an  ammono-acid.46  In  view  of  the  fact  that  nitrogen  is  tri-valent, 
the  acid  amides  are  dibasic  acids  in  contrast  with  the  corresponding  aquo- 
acids  which  are  mono-basic.  As  we  have  seen  in  an  earlier  chapter,  the 
acid  amides  are  soluble  in  ammonia  and  many  of  them  are  excellent  con- 
ductors of  the  electric  current.  It  has  been  shown  that  the  acid  amides 
and  imides  in  ammonia  possess  characteristic  acidic  properties;  that  is, 
they  react  with  the  metals  to  form  salts  and  hydrogen  and  with  .bases 
to  form  salts  and  ammonia.  Thus  we  have: 

Mg  +  CH3CONH2  =  CH3CONMg  +  H2, 

a  reaction  similar  to  that  obtained  with  acetic  acid  in  water.  The  acid 
amides  likewise  react  with  bases  in  ammonia  to  form  salts  and  water; 
for  example, 

CH3CONH2  +  (CH3)4NOH  =  CH3CONH(CH3)<N  +  H2O. 

Acid  amides  in  ammonia  solution  are  weaker  acids  than  the  correspond- 
ing oxy- acids  are  in  aqueous  solutions,  but  this  is  to  be  expected,  since 
the  dielectric  constant  of  ammonia  is  much  lower  than  that  of  water  and 
the  ionization  of  all  electrolytes  is  lower  in  ammonia  than  in  water. 
However,  as  may  be  seen  from  the  conductance  values  for  the  acid  amides 
in  ammonia  solution  as  given  in  an  earlier  chapter,  the  ionization  of 
certain  of  these  acids  in  ammonia  is  as  great  as  that  of  typical  salts  in 
this  solvent.  Relatively,  therefore,  the  acid  amides  are  as  strong  in 
ammonia  as  ordinary  acids  are  in  water.  It  is  interesting  to  point  out, 
in  this  connection,  that,  while  the  acid  amides  throughout  exhibit  acidic 
properties  in  ammonia  solution,  it  is  only  in  exceptional  cases  that  they 
exhibit  marked  acidic  properties  in  water.  The  reason  for  this  is  not 
well  understood,  but  it  seems  probable  that,  when  the  acid  amides  are 

48  Franklin,  Am.   Chem.  J.  3fi,  285    (191-2).     See  also  numerous  other  articles  by  the 
same  author  in  the  Am.  Chem.  J.  and  J.  Am.  Chem.  Soc. 


316        PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

dissolved  in  water,  the  basic  properties  of  the  nitrogen  come  into  play 
and  that  compounds  of  a  basic  nature  are  formed  similar  to  ammonium 
hydroxide,  which,  however,  are  ionized  only  to  an  exceedingly  small  ex- 
tent, in  view  of  the  electronegative  character  of  the  rest  of  the  molecule. 

As  has  already  been  pointed  out,  the  basic  amides,  as  for  example 
potassium  and  sodium  amides,  are  electrolytes  in  ammonia  solution  and, 
from  their  constitutional  relation  to  ammonia,  it  is  to  be  expected  that 
solutions  of  these  substances  will  exhibit  basic  properties  in  liquid  am- 
monia. This  is,  indeed,  the  case.  Potassium  amide,  dissolved  in  liquid 
ammonia,  exhibits  all  the  properties  characteristic  of  bases.  For  ex- 
ample, it  reacts  with  acids  to  form  salts  and  ammonia;  thus: 

CH3COOH  +  KNH2  =  CH3COOK  +  NH3. 

According  to  Franklin,  bases  of  this  type  are  called  ammono-bases. 
Obviously,  all  basic  amides  belong  to  this  class  of  substances. 

The  ammono-bases  react  not  only  with  aquo-acids  but  also  with 
ammono-acids.47  Thus,  an  ammono-acid  reacts  with  an  ammono-base 
to  form  an  acid  ammono-salt  and  ammonia,  according  to  the  equation: 

CH3CONH2  +  KNH2  =  CH3CONHK  +  NH3. 

It  is  interesting  to  note  that  the  color  reactions  characteristic  of  indi- 
cators are  likewise  found  reproduced  in  ammonia  solutions.48  Some 
indicators  exhibit  a  remarkably  sharp  end  point;  as,  for  example,  saf- 
franine.  The  nature  of  the  indicator  reactions  have  not,  as  yet,  been 
studied  in  detail. 

In  aqueous  solutions,  salts  of  weak  acids  and  bases  are  hydrolyzed 
owing  to  interaction  between  the  ions  of  the  solvent  with  those  of  the 
dissolved  salt.  So,  also,  in  ammonia  solutions,  the  salts  of  very  weak 
acids  and  bases  are  ammonolyzed;  that  is,  the  salt  reacts  with  the  sol- 
vent to  form  an  acid  and  a  base.  Unfortunately,  the  extent  to  which 
ammonia  is  ionized  into  H+  and  NH2~  ions  is  not  known.  In  all  likeli- 
hood, however,  the  concentration  of  these  ions  is  extremely  low,  since 
the  alkali  metals  are  soluble  in  liquid  ammonia  and  remain  in  solution 
for  extended  periods  of  time  with  only  a  slight  reaction,  according  to 
the  equation: 

Na  =  NaNH          H. 


If  the  concentration  of  the  hydrogen  ions  were  considerable,  this  reaction 
should  take  place  with  great  rapidity  just  as  the  corresponding  reaction 
takes  place  in  water.  That  hydrolysis  (or  ammonolysis)  actually  takes 


47  Franklin  and  Stafford,  Am.  Chem.  J.  28,  83   (1902). 
«8  Franklin  and  Kraus,  Am.  Chem.  J.  23,  277    (1900). 


OTHER  PROPERTIES.  OF  ELECTROLYTIC  SOLUTIONS  317 

place,  however,  has  been  definitely  shown.  As  a  consequence  of  the 
very  low  concentration  of  the  H+  and  NH2~  ions  in  ammonia,  it  is  only 
in  the  case  of  salts  of  extremely  weak  acids  or  bases  that  hydrolysis  has 
been  observed.  For  example,  when  mercuric  chloride  is  dissolved  in 
ammonia  the  following  reaction  occurs: 

HgCl2  +  NH2-  +  NH8  =  HgNH2Cl  +  NH4C1. 

In  this  case,  the  compound  HgNH2Cl  is  insoluble  and  is  precipitated. 
Obviously,  this  precipitation  proceeds  until  the  concentration  of  NH4C1 
is  sufficiently  great  to  bring  the  reaction  to  equilibrium.  The  addition 
of  an  ammonium  salt,  which  raises  the  concentration  of  the  NH4+  (hydro- 
gen) ions,  reverses  the  reaction,  causing  the  precipitate  to  go  into  solu- 
tion; while,  on  the  other  hand,  the  addition  of  an  ammono-base,  KNH2, 
for  example,  results  in  an  increased  precipitation.  In  most  instances, 
however,  salts  dissolve  in  ammonia  without  appreciable  ammonolysis. 
This  is  indicated  by  the  fact  that  in  many  cases  the  resulting  base  or 
basic  salt  is  practically  insoluble  and  even  a  small  degree  of  ammonolysis 
would  result  in  the  formation  of  a  precipitate.  Since  in  the  great  ma- 
jority of  cases  the  salts  yield  clear  solutions,  it  is  obvious  that  am- 
monolysis does  not  occur  to  an  appreciable  extent. 

A  considerable  number  of  reactions  have  been  studied  in  solvents  of 
very  low  dielectric  constants 49  such  as  benzene,  toluene,  etc.  Reactions 
in  these  solvents  often  take  place  readily  and  even  instantaneously.  As 
a  rule  the  salts  dissolved  are  heavy  metal  salts  of  the  higher  organic 
acids  such  as  the  oleates,  stearates,  etc.  It  has  been  claimed  that  solu- 
tions of  these  salts  are  non-conductors,  but  the  work  of  Cady  and 
Lichtenwalter  indicates  that,  while  -the  order  of  conductance  of  solutions 
of  salts  of  organic  acids  in  benzene  is  low  compared  with  that  of  ordi- 
nary solutions  of  electrolytes,  nevertheless,  benzene  solutions  conduct 
far  more  readily  than  does  the  pure  solvent.  In  the  case  of  a.metathetic 
reaction  with  hydrochloric  acid,  the  conductance  was  found  to  rise  largely 
before  precipitation,  due,  presumably,  to  the  relatively  greater  con- 
ductance of  the  more  concentrated  supersaturated  solution.  That  solu- 
tions of  salts  in  such  solvents  as  benzene  are  sufficiently  ionized  to  exert 
a  marked  influence  on  the  conductance  is  not  to  be  doubted. 

Metathetic  reactions  take  place  readily  in  solutions  in  solvents  of 
low  dielectric  constants  such  as  benzene,  but,  apparently,  these  reactions 
are  not  always  instantaneous.50  This  result  may  in  part  be  due  to  the 

«•  Kahlenberg,  J.  Phys.  Chem.  6,  1  (1902)  ;  Sammts,  ibid.,  10,  593  (1906);  Gates 
ibid.,  15,  97  (1911)  ;  Cady  and  Lichtenwalter,  J.  Am.  Chem.  Soc.  55,  1434  (1913)  ;  Cady 
and  Baldwin,  ibid..  43,  646  (1921). 

80  Cady  and  Lichtenwalter,  loc.  cit. 


318        PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

formation  of  supersaturated  solutions.  Reactions  between  silver  per- 
chlorate  and  'hydrochloric  acid,  mercuric  chloride  and  trimethyltin 
chloride  take  place  instantaneously  in  benzene.51  Small  amounts  of 
water  greatly  influence  the  conductance  of  solutions  of  this  type. 

While  these  results  are  in  good  agreement  with  the  ionic  hypothesis, 
it  cannot  be  said  that  reactions  cannot  take  place  between  the  un- 
ionized molecules.  For  example,  methyl  iodide  precipitates  silver  iodide 
in  solutions  of  silver  perchlorate  in  benzene.  If  reactions  of  this  type 
are  ionic,  we  must  modify,  somewhat,  our  notions  relative  to  the  nature 
of  organic  compounds.  Yet  not  a  few  facts  are  in  excellent  agreement 
with  such  a  view. 

Reactions  of  the  electrolytic  type,  in  which  one  metal  is  substituted 
by  another  more  electropositive  metal,  have  also  been  studied  in  sol- 
vents of  low  dielectric  constants.52  Such  reactions  often  take  place 
readily.  It  appears  not  unlikely  that  they  are  in  fact  electrolytic.  The 
properties  of  solutions  of  substances  of  the  electrolytic  type  in  solvents 
of  low  dielectric  constant  have  received  all  too  little  attention.  The 
data  so  far  are  too  fragmentary  to  warrant  drawing  conclusions  of  a 
general  nature,  but  it  is  not  to  be  doubted  that  the  study  of  such  systems 
will  lead  to  important  results.  Electrolytic  phenomena  are  not  confined 
to  solvents  of  high  dielectric  constant.  Evidence  is  constantly  accumu- 
lating which  supports  the  view  that  all  fluid  media  possess,  in  some 
degree,  the  power  of  forming  electrolytic  solutions  under  suitable  con- 
ditions. 

9.  Factors  Influencing  lonization.  a.  The  Ionizing  Power  of  Sol- 
vents in  Relation  to  Their  Constitution.  Since,  as  we  have  seen,  the 
ionizing  power  of  a  solvent  is  largely  determined  by  its  dielectric  con- 
stant, it  follows  that,  in  seeking  to  determine  possible  relations  between 
the  constitution  of  a  substance  and  its  ionizing  power,  we  should  seek 
for  relations  between  the  dielectric  constant  and  the  constitution  of  the 
substance  in  question.  Water,  hydrocyanic  acid  and  formamide  have 
the  highest  dielectric  constants  of  substances  so  far  investigated. 

The  nature  of  the  relation  between  the  dielectric  constant  and  the 
constitution  of  liquid  media  is  not  clear.  There  is,  however,  an  obvious 
relation  between  the  dielectric  constant  of  the  hydrogen  derivatives  of 
the  elements  and  their  position  in  the  periodic  system.  The  hydrogen 
derivatives  of  the  first  members  of  the  various  groups  invariably  exhibit 
a  dielectric  constant  much  greater  than  that  of  the  following  members. 
Similarly,  the  dielectric  constant  of  the  hydrogen  derivatives  of  elements 

61  Observations  by  Messrs.  Callis  and  Greer  in  the  Author's  Laboratory. 
"Gates,  loc.  cit. 


OTHER  PROPERTIES  OF  ELECTROLYTIC  SOLUTIONS  319 

in  a  given  series  increases  with  the  order  of  the  group.  Thus,  water 
has  a  dielectric  constant  of  approximately  80  and  is  an  excellent  ioniz- 
ing agent,  while  hydrogen  sulphide  has  a  dielectric  constant  of  10  and 
is  a  relatively  poor  ionizing  agent.  Ammonia  at  its  boiling  point  has 
a  dielectric  constant  of  22  and  is  a  moderately  good  ionizing  agent.  In 
the  seventh  group,  hydriodic  acid  has  a  dielectric  constant  of  2.9,  hydrp- 
bromic  acid  of  6.3,  and  hydrochloric  acid  of  9.5.  As  we  approach  the 
derivatives  of  the  upper  members  of  this  group,  their  dielectric  constant 
and  their  ionizing  power  increase.  The  dielectric  constant  of  hydrogen 
fluoride  is  not  known  but  it  is  known  to  be  an  excellent  ionizing  agent. 
Moissan,  for  example,  prepared  fluorine  by  the  electrolysis  of  fluorides 
in  liquid  hydrogen  fluoride.  'It  seems  not  improbable  that  the  dielectric 
constant  of  hydrofluoric  acid  is  greater  than  that  of  water.  At  any  rate, 
in  passing  from  ammonia  to  water,  the  dielectric  constant  increases  from 
22  to  80,  and  it  is,  therefore,  not  improbable  that  the  dielectric  constant 
of  hydrogen  fluoride  is  higher  than  that  of  water.  The  dielectric  con- 
stant of  many  organic  and  inorganic  substances  containing  oxygen,  nitro- 
gen, chlorine  and  sulphur  is  relatively  high.  Such  substances  in  the 
liquid  state  possess  the  power  of  dissolving  salts  and  of  forming  conduct- 
ing solutions  with  them.  It  is  unnecessary  to  give  here  a  detailed  list  of 
these  substances. 

With  increasing  temperature,  the  dielectric  constant  of  all  substances 
decreases.  The  dielectric  constants  of  a  number  of  substances  have  been 
measured  through  the  critical  point.53  These  include  sulphur  dioxide, 
ether,  ethylchloride,  and  hydrogen  sulphide.  For  these  substances  the 
dielectric  constant  just  beyond  the  critical  point  is  2.1,  1.52,  4.68  and  2.7 
respectively.  A  striking  result,  here,  is  the  relatively  high  value  of  the 
dielectric  constant  of  ethylchloride  at  the  critical  point  relative  to  its 
value  at  lower  temperatures.  Thus  at  59°  its  value  is  6.29,  which  de- 
creases to  the  value  given  above  at  186°.  Evidently  the  variation  of 
the  dielectric  constant  with  the  temperature  depends  largely  upon  the 
nature  of  the  solvent.  Corresponding  to  the  low  value  of  the  dielectric 
constant  of  sulphur  dioxide,  the  conductance  of  solutions  of  electrolytes  in 
this  solvent  falls  to  very  low  values.  The  same  is  true  of  ammonia  solu- 
tions, although  in  this  solvent  the  conductance  above  the  critical  point 
has  a  readily  measurable  value.  The  conductance  of  typical  salts  in 
ethylchloride  has  not  been  measured,  but  that  of  mercuric  chloride 
solutions,  whose  ionization  is  usually  relatively  low,  is  greater  than 
that  of  solutions  of  typical  electrolytes  in  sulphur  dioxide  under 
corresponding  conditions.  Judging  by  the  conductance  of  solutions 

"Eversheim,  Ann.  d.  Phys.  8,  539   (1902)  ;  ibid.,  13f  492   (1904). 


320        PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

in  the  critical  regions,  solvents  which  have  a  dielectric  constant  greater 
than  26  at  ordinary  temperatures  have  fairly  high  dielectric  con- 
stants in  the  critical  region;  and,  probably,  the  higher  the  dielectric 
constant  of  solvents  of  this*  type,  the  greater  the  dielectric  constant  in 
the  critical  region.  In  all  likelihood,  the  dielectric  constant  of  water  in 
the  critical  region  is  fairly  high.  Unfortunately,  there  are  very  few  data 
available  on  the  relation  between  the  dielectric  constant  and  the  variables 
which  determine  the  condition  of  the  solvent. 

Among  solvents  of  high  dielectric  constant,  only  solutions  in  water 
have  been  measured  with  any  considerable  degree  of  precision.  The 
conductance  of  solutions  in  hydrocyanic  acid  indicates  that  the  behavior 
of  solutions  of  electrolytes  in  this  solvent  is  similar  to  that  in  aqueous 
solutions,  but  available  data  are  not  sufficiently  accurate  to  make  it 
possible  to  determine  the  precise  form  of  the  conductance  curve.  Fur- 
ther data  on  the  properties  of  solutions  in  solvents  of  high  dielectric  con- 
stant are  much  needed. 

b.  The  Relation  between  the  lonization  Process  and  the  Constitution 
of  the  Electrolyte.  While  the  ionization  of  an  electrolyte  is,  in  the  first 
place,  largely  dependent  on  the  dielectric  constant  of  the  solvent  medium, 
the  strongest  typical  electrolytes  are  probably  ionized  in  all  solvents, 
provided  they  are  sufficiently  soluble,  but  in  solvents  of  very  low  dielec- 
tric constant  ionization  is  appreciable  only  at  high  concentrations.  The 
typical  inorganic  salts  are  not,  as  a  rule,  sufficiently  soluble  in  solvents 
of  low  dielectric  constant  to  yield  solutions  which  conduct  the  current 
readily.  However,  salts  of  various  organic  bases,  such  as  the  substituted 
ammonium  salts  5*  are  soluble  in  solvents  of  low  dielectric  constant  and 
conduct  the  current. 

The  dielectric  constant  is  only  one  of  the  factors  governing  the  ion- 
ization process.  For  ionization  is  largely  dependent  upon  the  nature  of 
the  second  component.  For  certain  substances,  which  we  ordinarily  class 
as  the  typical  salts,  the  dielectric  constant  of  the  solvent  medium  is 
largely  determinative  of  the  ionization,  but  even  here  we  find  that  in 
non-aqueous  solvents  the  ionization  may  vary  greatly  for  salts  whose 
ionization  values  are  practically  identical  in  water.  This  is  true  of  solu- 
tions in  ammonia  and  still  more  so  of  solutions  in  acetone.  In  these 
solvents,  the  characteristic  properties  of  the  electrolyte  persist  even  down 
to  the  lowest  concentrations  for  which  measurements  exist  and  these  con- 
centrations are  much  lower  than  those  in  aqueous  solutions.  No  theory 
of  electrolytic  solutions  can  be  looked  upon  as  adequate  which  does  not 
render  an  account  of  this  very  common  property  of  these  solutions. 

"Walden,  Bull.  Acad.  Imp.  dee  Sci,,  p.  U07,  No.  16  (1913),  VI  series. 


OTHER  PROPERTIES  OF  ELECTROLYTIC  SOLUTIONS  321 

In  general,  compounds  between  strongly  electronegative  and  strongly 
electropositive  constituents  are  electrolytes  both  in  solution  and  in  the 
fused  state.  This  includes  not  only  salts  of  strong  acids  and  bases  but 
also  salts  of  weaker  acids  and  bases.  Thus,  the  ammonium  salts  are  ex- 
cellent conductors  both  in  solution  and  in  the  fused  state.  The  same  is 
true  of  salts  of  organic  bases.  Here,  however,  we  find  a  few  marked  excep- 
tions. Thus,  the  trimethylin  halides,  (CH3)3SnX  are 'normally  ionized 
in  aqueous  solution,  but  are  ionized  much  less  than  other  typical  salts 
in  alcohol  and  still  less  in  acetone.  In  nitrobenzene  and  benzonitrile 
these  salts  are  not  ionized  at  all,  although  these  solvents  have  dielectric 
constants  higher  than  that  of  alcohol.  Finally,  these  salts  are  not  appre- 
ciably ionized  in  the  liquid  state.55  It  is  evident  that  we  have  here  an 
extreme  case  of  individuality  in  an  electrolytic  substance. 

In  many  cases,  the  electrolytic  properties  of  a  solution  are  due  to 
interaction  between  the  solvent  and  the  solute  whereby  an  electrolyte 
is  produced.  Thus,  the  acids  are  electrolytes  in  solution  but  in  the  pure 
state  they  exhibit  a  very  low  conductance.  Indeed,  the  acids  are  electro- 
lytes only  in  what  may  be  termed  basic  solvents;  that  is,  solvents  capable 
of  forming  salts  or  salt-like  substances  on  addition  to  an  acid.  Ammonia 
and  ammonium  salts  are  typical  examples  of  a  solvent  and  a  salt  of  this 
type.  Solutions  of  the  acids  in  water  and  the  alcohols  probably  depend 
for  their  electrolytic  properties  on  the  formation  of  similar  complexes 
between  the  acid  and  the  solvent.56  When  acids  are  dissolved  in  non- 
basic  solvents,  such  as  sulphur  dioxide  or  nitrobenzol,  the  resulting  solu- 
tions exhibit  a  very  low  conductance,  provided  the  solvent  is  quite  dry. 
Doubtless,  similar  considerations  hold  for  solutions  of  acidic  substances, 
such  as  the  acid  amides  in  ammonia.57  So,  also,  solutions  of  many 
organic  oxygen  and  nitrogen  compounds  in  the  liquid  halogen  acids  owe 
their  electrolytic  properties  to  the  formation  of  a  more  or  less  stable 
complex  between  the  dissolved  substance  and  the  acid  solvent.  The 
inorganic  bases,  while  intimately  related  to  the  acids  from  the  standpoint 
of  their  constitution  in  aqueous  solution,  are  otherwise  to  be  classed  as 
salts.  The  -properties  which  they  exhibit  are  throughout  characteristic 
of  salts. 

In  general,  compounds,  in  which  distinctly  electropositive  and  electro- 
negative constituents  are  not  present,  are  not  electrolytes;  or,  at  any 
rate,  in  a  fused  state  they  are  relatively  poor  conductors  of  the  electric 

65  Observations  by  Mr.  C.  C.  Callis  in  the  Author's  Laboratory. 

58  Kendall  and  Gross,  J.  Am.  Chem.  Soc.  Jtf,  1426  (1921),  have  investigated  the  con- 
ductance  of  mixtures  of  acids  with  esters,  ketones  and  other  acids  and  have  found  unmis- 
takable signs  of  the  formation  of  compounds. 

57  The  acid  amides  do  not  conduct  in  water  probably  owing  to  the  fact  that  these 
substances  act  as  very  weak  bases  in  water,  whose  acidic  properties  are  much  greater 
than  those  of  ammonia. 


322        PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

current  and  in  solution  their  conductance  is  low.  Nevertheless,  solutions 
of  non-polar  substances  may  exhibit  marked  electrolytic  properties.  So, 
for  example,  solutions  of  iodine  bromide,  iodine  trichloride,  iodine,  phos- 
phorus trichloride,  phosphorus  pentabromide,  etc.,  conduct  the  current  to 
a  measurable  extent  in  sulphur  dioxide,  arsenic  trichloride,  sulfuryl  chlo- 
ride, nitrobenzene,58  etc.  So,  also,  for  example,  solutions  of  iodine  in 
bromine  conduct  the  current.  Walden  has  suggested  that  in  these  solu- 
tions one  electronegative  atom  functions  as  anion  and  another  as  cation. 
For  example,  he  assumes  that  a  reaction  of  the  type: 

I,  =  !*  +  !-, 

takes  place  when  iodine  is  dissolved  in  sulphur  dioxide.  The  investiga- 
tions of  Bruner  and  Galecki 59  and  Bruner  and  Bekier 60  have  shown  that, 
in  sulphur  dioxide  and  nitrobenzol,  the  halogens  and  their  compounds 
are  not  constituents  of  the  positive  ions.  At  any  rate,  on  electrolyzing 
such  solutions,  the  negative  element  may  be  concentrated  at  the  anode. 
The  nature  of  the  cation  in  these  solutions  is  uncertain,  but  there  appears 
to  be  little  doubt  that  the  electronegative  constituent  is  associated  with 
the  anion.  Apparently,  the  electrolytic  properties  of  these  solutions  are 
due  to  the  formation  of  a  complex  between  the  strongly  electronegative 
element  or  compound  and  the  solvent,  in  which,  presumably,  the  solvent 
molecule,  in  part  at  least,  functions  as  cation. 

So  far  as  the  electrolytic  properties  of  their  compounds  are  concerned, 
strongly  electronegative  elements  or  groups  of  elements  may  not  function 
as  cations,  although  it  is  possible  that  in  certain  cases  they  may  be  asso- 
ciated with  the  cation  in  the  form  of  a  complex  ion,  as  is  the  case,  for 
example,  with  iodine  in  the  intermediate  ion  of  cadmium  iodide  in 
aqueous  solution.  On  the  other  hand,  as  we  have  already  seen,  metals, 
which  normally  are  electropositively  charged  in  their  compounds  with 
more  electronegative  elements,  may,  under  certain  conditions,  function  as 
anions.  For  example,  sodium  and  lead  in  ammonia  react  to  form  a  solu- 
tion in  which  the  two  elements  are  present  in  the  ratio  of  2.25  atoms  of 
lead  to  one  atom  of  sodium,  when  metallic  lead  is  present  in  excess.61 
On  electrolysis  of  these  solutions,  lead  is  precipitated  on  the  anode.  The 
properties  of  these  complex  anions  have  already  been  discussed. 

68  Walden,  Ztschr.  f.  phj/s.  Chem.  tf,  385  (1903). 

»  Bruner  and  Galecki,  Ztschr.  f.  phya.  Chem.  8$,  513   (1913). 

60 Bruner  and  Bekier,  i&id..  8},  570  (1913). 

"Kraus,  J.  Am.  Chem.  Soc.  29,  1557   (1907)  ;  Smyth,  iWd.,  39,  1299   (1917), 


Chapter  XII. 
Theories  Eelating  to  Electrolytic  Solutions. 

1.  Outline  of  the  Problem  Presented  by  Solutions  of  Electrolytes. 
The  problem  of  electrolytic  conduction  presents  a  twofold  aspect  depend- 
ing upon  the  point  of  view  from  which  it  is  approached.  On  the  one 
hand,  we  are  concerned  with  certain  well  defined  equilibria,  the  laws 
governing  which  it  is  attempted  to  discover;  on  the  other,  we  are  con- 
cerned with  the  mechanism  of  the  process  whereby  the  conduction  of  the 
electric  current  is  effected.  In  the  first  case  the  principles  governing 
equilibria  in  mixtures  are  applied,  supported  by  various  auxiliary  assump- 
tions which  are  necessary  if  an  explicit  solution  of  the  problem  is  to  be 
reached.  These  assumptions  usually  involve  the  equation  of  state  of 
the  system,  the  precise  form  of  which  is  not  known.  A  general  solution, 
therefore,  cannot  be  reached  by  this  method.  In  order  to  disclose  the 
mechanism  of  the  conduction  process,  a  knowledge  of  the  forces  acting 
between  the  conducting  particles  and  their  surroundings  is  required. 
Since  the  laws  governing  these  forces  are  not  known,  a  solution  is  not 
possible  by  this  method.  Furthermore,  if  a  force  function  is  assumed, 
a  solution  can  be  reached  only  by  the  application  of  statistical  methods 
and  these  methods  have  not  been  developed  to  a  point  where  their  appli- 
cation to  electrolytic  systems  can  be  made  with  any  degree  of  certainty. 
In  either  case,  therefore,  a  point  is  soon  reached  where  the  results  ob- 
tained are  little  more  than  conjectures.  The  probable  correctness  of  the 
results  obtained  may  be  checked  by  comparison  with  experiment.  In 
practice  it  is  often  found  that,  while  the  results  of  one  method  agree 
fairly  well  among  themselves,  they  disagree  with  those  obtained  by  the 
alternative  method.  That  the  two  methods  must  lead  to  results  which 
are  in  mutual  agreement  is  not  to  be  doubted.  Lack  of  agreement  indi- 
cates that  various  assumptions  made  are  not  permissible. 

It  may  be  expected  that  a  solution  of  the  problem  will  first  be  reached 
for  mixtures  where  the  concentration  of  the  electrolytic  component  is  so 
%low  that  various  effects,  due  to  the  interaction  of  the  ions  and  other  mo- 
lecular species  present,  become  negligible.    Here,  however,  the  difficulty 
arises  that  experimental  data  become  very  uncertain.    Nevertheless,  ap- 

323 


324        PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

preciable  progress  has  been  made  in  this  direction.  In  dilute  solutions  of 
weak  electrolytes,  the  ionic  theory  has  met  with  marked  success  and, 
while  it  may  be  expected  that  here,  too,  the  theory  will  have  to  be 
materially  modified  when  a  final  solution  of  the  problem  has  been  reached, 
the  mutual  consistency  of  the  results  obtained  indicates  that  a  consider- 
able measure  of  truth  underlies  the  ionic  theory  as  formulated.  This 
important  fact  should  not  be  lost  sight  of  in  developing  a  more  general 
theory  of  electrolytic  solutions. 

The  inapplicability  of  the  law  of  mass  action  in  its  simple  form  to 
relatively  dilute  solutions  of  strong  electrolytes  has  led  to  many  contro- 
versies relative  to  the  nature  of  these  solutions.  On  the  one  hand,  it  has 
been  suggested  that  such  solutions  are  completely  ionized  at  all  concen- 
trations ; *  and,  on  the  other,  that  they  are  not  ionized  at  all.2  Still  other 
theories  attempt  to  relate  these  solutions  with  colloidal  systems.3  The 
proposed  theories  may  be  grouped  into  three  classes:  (1)  theories  which 
are  derived  by  combining  with  thermodynamic  principles  auxiliary 
assumptions,  which,  in  part  at  least,  are  of  an  empirical  nature;  (2) 
theories  in  which  the  interionic  forces  due  to  the  charges  are  taken  into 
account;  and  (3)  theories  of  a  miscellaneous  nature  which  as  a  rule  are 
of  a  qualitative  character. 

2.  Electrolytic  Solutions  from  the  Thermodynamic  Point  of  View. 
a.  Scope  of  the  Thermodynamic  Method.  If  equilibria  exist  in  solu- 
tions of  electrolytes,  as  we  have  reason  to  believe,  then  such  solutions 
must  be  subject  to  the  thermodynamic  principles  governing  equilibria. 
That  equilibria,  in  fact,  exist  in  electrolytic  systems  is  not  to  be  doubted, 
since  in  no  other  class  of  systems  do  reactions  proceed  so  rapidly  to  a 
definite  condition.  In  most  instances,  it  is  not  possible  to  measure  the 
speed  with  which  reaction  takes  place  in  these  solutions.  The  first 
assumption  which  arises  in  the  detailed  application  of  the  principles  of 
thermodynamics  to  equilibria  in  solutions  of  electrolytes  is  that  of  the 
precise  nature  of  the  reaction  involved.  It  is  obvious  that,  before  equi- 
libria of  the  electrolytic  type  can  be  treated  comprehensively,  the  nature 
of  the  reactions  involved  must  be  definitely  established.  All  considera- 
tions in  which  these  reactions  are  involved  are  necessarily  subject  to 
uncertainty,  since  it  has  not  been  found  possible  to  establish,  definitely, 
whether  or  not  un-ionized  molecules,  as  well  as  ions,  exist  in  electrolytic 
solutions.  The  nature  of  the  reaction  being  assumed,  the  thermodynamic 
treatment  of  electrolytic  solutions  is  comparatively  simple,  so  far  as  the 
thermodynamic  considerations  themselves  are  concerned.  When,  how- 

1  Ghosh,  Trans.  Chem.  Soc.  UL3.  449   (1918). 
*Snethlage,  Ztschr.  f.  phys.  Chem.  90,  1    (1915). 
•  Georgievics,  Ztschr.  f.  phys.  Chem.  90,  341   (1915). 


THEORIES  RELATING  TO  ELECTROLYTIC  SOLUTIONS          325 

ever,  the  concentrations  of  the  various  constituents  present  in  the  solu- 
tion are  such  that  the  laws  of  ideal  systems  are  no  longer  applicable 
within  the  limits  of  experimental  error,  a  general  solution  of  the  problem 
is,  at  the  present  time,  not  possible.  In  other  words,  the  general  solution 
of  the  problem  involves  a  knowledge  of  the  equation  of  state  of  the 
system.  According  to  the  equilibrium  principle  of  Gibbs,  a  system  will 
be  in  stable  equilibrium  when  the  entropy  is  a  maximum.  For  many 
purposes  it  is  more  convenient  to  introduce  derived  functions  such  as  the 
Gibbsian  functions  \p  and  £  in  place  of  the  entropy.  For  a  mixture  of  any 
number  of  components  in  a  system,  not  subject  to  reaction,  the  free  energy 
is  given  by  the  equation: 


[(\-x-y-z-  •  •)  log  (1-x-y-z--) 

(98)  v 

+  x  log  x  +  y  log  y  +  z  log  z  +  •••]+  F(xyz  .  .  T), 

where  x,  y,  z,  etc.,  represent  the  amounts  of  the  various  constituents  pres- 
ent per  gram  mol  of  the  mixture.  The  term  F  (xyz  .  .  T)  is,  in  general,  a 
determinate  function  of  temperature  and  a  linear  function  of  xyz  .  .  . 
The  term  (  pdv  is  a  function  of  the  concentrations  xyz.  .,  and  represents 

Jv 

the  work  done  in  bringing  the  system  from  a  condition  in  which  the  laws 
of  an  ideal  system  are  obeyed  to  the  condition  in  which  the  system  obeys 
any  given  equation  of  state.4  It  is  obvious  that  the  condition  for  equi- 
librium, d\\>  —  0,  may  at  once  be  applied  if  the  equation  of  state  is 
known,  while,  if  the  equation  of  state  is  not  known,  the  problem  is  neces- 
sarily insoluble,  since  it  is  not  possible  to  evaluate  the  integral  in  ques- 
tion. When  reaction  takes  place  between  various  constituents  present  in 
the  mixture,  the  condition  for  equilibrium  leads  to  the  equation: 

(99)  2AT  =  0, 
where 

(100)  .M 


Here  ra  is  the  molecular  weight  of  the  constituent  and  \i  is  the  thermo- 
dynamic  potential  defined  according  to  Gibbs.5  The  molecular  potential 
M,  of  a  constituent,  is  given  by  an  equation  of  the  form: 


(101)  M  =  RTlogx  +  F(vT  xyz..) 

where  F(vT  xyz..)  is  a  function  of  the  composition  of  the  system,  as 
well  as  of  volume  and  temperature,  except  when  the  equation  of  state  of 

4  van  der  Waals-Kohnstamm,   "Lehrbuch   der   Thermodvnamik  "   Vol    2 
•Gibbs,  Scientific  Papers,  Vol.  1,  pp.  92  et  seq.   (1912). 


326        PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

the  system  fulfills  the  condition  pv  =  RT,  in  which  case  the  only  manner 
in  which  the  concentration  is  involved  in  the  expression  for  the  thermo- 
dynamic  potential  is  in  the  logarithmic  term  of  the  above  equation.  In 
order  to  evaluate  the  term  F(vT  xyz.  .  )  it  is  necessary  to  know  the  equa- 
tion of  state  of  the  system,  since  the  value  of  M  as  given  by  the  equation: 


,,02,  «  =  »-. 

obviously  involves  the  term    f  pdv  ,  which  cannot  be  evaluated  without 

}v 

a  knowledge  of  the  equation  of  state.  The  equations  of  state  for  mix- 
tures of  ordinary  liquids  are  comparatively  complex,  and  a  general  solu- 
tion of  the  problem  has  not  been  effected,  even  for  liquids  of  simple  type  ; 
while,  in  the  case  of  mixtures  of  substances  whose  equations  of  state  are 
comparatively  complex,  even  an  approximate  solution  has  been  little  more 
than  attempted.  This  subject  has  been  treated  in  detail  by  van  der 
Waals.6 

b.  Jahn's  Theory  of  Electrolytic  Solutions.  Nernst  7  and  Jahn  8 
attempted  to  solve  the  problem  of  solutions  of  strong  electrolytes  by 
introducing  various  correction  terms.  Since  the  true  equation  of  state 
for  mixtures  containing  electrolytes  is  not  known,  even  approximately, 
it  is  obvious  that  these  theories  necessarily  involve  assumptions  of  an 
arbitrary  nature.  These  assumptions  must  contain  within  them  the 
equivalent  of  an  equation  of  state.  In  how  far  these  assumptions  are 
allowable  may  be  ascertained  by  comparing  the  consequences  of  these 
theories  with  the  experimental  facts.  Jahn  set  up  the  conditions  for 
equilibrium,  employing  as  a  criterion  for  equilibrium,  the  variation  of 
Planck's  function: 

It  is  on  the  whole  immaterial  what  function  is  employed  as  criterion  for 
equilibrium,  provided,  always,  that  it  fulfills  the  conditions  of  a  charac- 
teristic function.9  These  functions  involve  the  energy  of  the  system  and, 
in  order  that  the  condition  for  equilibrium  may  be  solved,  it  is  necessary 
to  have  an  expression  for  the  energy  of  the  system  in  terms  of  its  com- 
position. In  the  case  of  ideal  systems,  Dalton's  law  may  be  assumed  to 
hold,  in  which  case  the  energy  of  a  mixture  of  substances  is  equal  to  the 
sum  of  the  energies  of  its  constituents.  Jahn  assumed  an  equation  for 

•  van  der  Waals-Kohnstamm,  loc.  cit. 
'Nernst,  Ztschr.  f.  phys.  Chem.  38,  487  (1901). 
•Jahn,  Ztschr.  1.  phys.  Chem.  41,  257   (1902). 
•Gibbs,  Scientific  Papers  1,  pp.  85  et  seq.   (1906). 


THEORIES  RELATING  TO  ELECTROLYTIC  SOLUTIONS          327 

the  energy  containing  cross  terms  due  to  forces  acting  between  the  dif- 
ferent molecular  species  present  in  the  mixture.  This  assumption,  which 
is  necessary  for  a  solution  of  the  problem  by  this  method,  is  obviously 
an  arbitrary  one.  Proceeding  in  this  way  Jahn  obtains,  for  a  system  of 
electrolytes  in  equilibrium,  the  equation: 

(C-)2 
(103)  log  -J-  =  (a  +  fa)C  +  log  tfo, 


where  a  and  (3  are  constants.  The  constancy  of  the  functions  ct  and  (3 
however,  depends  upon  the  original  assumption  made  with  regard  to  the 
manner  in  which  the  energy  of  the  system  is  dependent  upon  its  composi- 
tion, and,  if  a  different  assumption  had  been  made,  it  would  have  led  to  a 
corresponding  variation  in  the  resulting  equation.  Methods  of  this  kind 
are  correct  enough  thermodynamically,  but,  in  order  that  they  may  lead 
to  results  which  may  be  tested  experimentally,  an  assumption  must  be 
made,  and  this  assumption  is,  in  general,  arbitrary  in  its  nature.  In  this 
sense,  therefore,  the  results  of  these  methods  are  to  be  looked  upon  as 
being  purely  empirical  in  character,  unless  evidence  of  an  a  priori  nature 
can  be  adduced  in  favor  of  the  assumptions  made.  In  all  cases,  the  cor- 
rectness of  the  assumptions  may  be  tested  by  comparing  the  resulting 
equations  with  the  experimental  values.  Taking  the  equation  of  Jahn, 
it  is  easy  to  make  a  comparison  with  experiment. 

This  equation  obviously  involves  four  constants ;  namely,  a,  (3  and  K0, 
together  with  A0,  the  limiting  value  of  the  equivalent  conductance.  The 
equation  is  a  fairly  complex  one  and  it  is  not  easy  to  extrapolate  for  the 
value  of  A0  on  the  basis  of  this  equation,  but  it  may  safely  be  assumed 
that,  in  the  case  of  potassium  chloride,  the  conductance  of  whose  solutions 
has  been  measured  to  2  X  10'5  normal,  the  true  value  of  AO  does  not 
differ  materially  from  that  ordinarily  assumed.  At  higher  concentra- 
tions, at  any  rate,  a  slight  error  in  the  value  of  A0  will  cause  a  relatively 
small  change  in  the  distribution  of  the  points.  Assuming  the  value  of 
A0,  and  calculating  the  values  of  the  function  K'  at  three  concentrations, 
it  is  possible  to  evaluate  the  constants  a,  p  and  K0.  The  values  of  a  and 
P  being  known,  the  equation  may  be  tested  by  plotting  values  of  log  K 
against  those  of  (a  +  py)  C.  This  plot  should  yield  a  linear  relation, 
but,  in  fact,  leads  to  results  inconsistent  with  the  experimental  values. 
The  value  of  K'  has  a  maximum  in  the  neighborhood  of  0.05  normal, 
after  which  it  decreases  rapidly.  The  equation  as  calculated  for  potas- 
sium chloride  at  18°  is  as  follows: 

log  K'  =  2.5935  +  (592.8  — 498.7y)C. 


328        PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

While  Jahn's  equation  has  not  been  tested  in  the  case  of  non-aqueous 
solutions,  it  is  easy  to  see  that  it  cannot  hold  generally.  For  example, 
f or  m  =  1  in  Equation  11,  the  function  K'  varies  practically  as  a  linear 
function  of  the  ion  concentration.  Such  an  equation  will  not  reduce  to 
the  form  of  that  of  Jahn. 

That  Jahn's  equation  should  not  hold  is  in  no  wise  surprising,  since- 
the  assumptions  underlying  it  are  of  an  arbitrary  nature.  It  is  improb- 
able that  the  free  energy  of  electrolytic  solutions  may  be  determined  as  a 
function  of  concentration  without  the  aid  of  an  equation  of  state.  In 
other  words,  the  chance  of  finding  the  correct  equation  by  mere  accident 
would  appear  to  be  vanishingly  small.  The  method  of  Nernst  does  not 
differ  materially  from  that  of  Jahn  and  leads  to  a  similar  result. 

c.  Comparison  of  the  Thermodynamic  Properties  of  Electrolytes. 
Inconsistencies  in  the  Older  Ionic  Theory.  While  the  application  of 
thermodynamic  principles  yields  no  information  relative  to  the  mecha- 
nism involved  in  electrolytic  solutions,  these  principles  when  combined 
with  other  hypotheses  lead  to  consequences  which  admit  of  verification. 

The  bearing  of  thermodynamics  on  the  theory  of  electrolytic  solutions 
was  long  neglected  and  has  often  been  misinterpreted.  So,  for  example, 
the  correspondence  between  the  ionization  values  as  derived  from  con- 
ductance and  from  osmotic  measurements  was  looked  upon  as  lending 
support  to  the  older  ionic  theory.  As  Nernst 10  pointed  out,  this  apparent 
confirmation  of  the  ionic  theory  constitutes,  in  fact,  one  of  the  chief 
obstacles  in  the  path  of  its  acceptance. 

Insofar  as  electrolytic  solutions  constitute  systems  in  which  equilibria 
prevail,  thermodynamic  principles  are  applicable.  It  is  evident,  how- 
ever, that  the  laws  of  dilute  solutions  are  not  applicable  to  these  systems 
at  ordinary  concentrations.  Aside  from  a  few  very  general  relations, 
the  application  of  thermodynamic  principles  alone  can  furnish  us  very 
little  information  relative  to  the  nature  of  these  solutions.  The  general 
problem  is  to  express  the  potentials  of  the  various  constituents  in  terms 
of  the  independent  variables  of  the  system;  that  is,  of  the  concentrations 
of  the  various  substances  present.  Since  statistical  and  other  methods 
have  not  been  developed  to  a  point  where  they  enable  us  to  determine  the 
equation  of  state  of  these  systems,  the  problem  at  the  present  time  can 
be  attacked  only  by  experimental  methods.  Fortunately,  the  potentials 
of  electrolytes  in  solution  may  be  determined  readily  and  with  a  rela- 
tively high  degree  of  precision.  The  values  of  the  potentials  as  thus 
determined  may  be  treated  by  graphical  or  other  empirical  methods;  and, 
while  the  theoretical  relation  between  the  potentials  and  the  concentra- 

«•  Nernst,  Ztschr.  f.  phys.  Chem.  38f  493   (1901)  ;  Jahn,  iUd.,  38,  125    (1901). 


THEORIES  RELATING  TO  ELECTROLYTIC  SOLUTIONS          329 

tions  of  the  constituent  electrolytes  remains  undisclosed,  the  form  of  the 
function  may  be  determined.  At  the  same  time,  the  values  of  the  poten- 
tials of  different  electrolytes  may  be  compared  and  relationships  brought 
to  light  which  are  of  practical  importance,  even  though  their  theoretical 
significance  may  not  be  apparent.  Our  knowledge  of  electrolytes  from 
this  point  of  view  is  restricted  to  aqueous  solutions.  In  view  of  the  fact 
that  many  properties  of  electrolytic  solutions  are  greatly  modified  in 
solvents  of  lower  dielectric  constant,  and  since  the  similarity  in  the  be- 
havior of  dilute  aqueous  solutions  of  different  electrolytes  is  not  often 
found  in  other  solvents,  any  generalization  of  the  results  obtained  in 
aqueous  solutions  must  be  made  with  caution. 

The  Thermodynamic  Method.  The  significance  of  the  results  ob- 
tained from  an  examination  of  the  thermodynamic  properties  of  electro- 
lytic solutions  will  be  better  understood  if  treated  without  reference  to 
detailed  methods.  Let  us  assume  that  we  have  a  solution  in  which  the 
following  reaction  takes  place: 

Mi  +  Mi  +••••-=  NI'^I'  +  **'**'  +  '" 
The  condition  for  equilibrium  in  such  a  solution  is: 

(104)  SnAf  =  Sn'JIf'  . 

The  potential  sum  for  the  constituents  on  either  side  of  the  reaction  equa- 
tion may  be  expressed  by  a  function  of  the  form: 


(105)  2nM  -  F(C1}C2).  .  .C/AV  •  •), 

where  C1}C2,.  .  .C/A',.  .  .  are.  independent  variables.  If  any  of  these 
variables  are  not  independent,  a  relation  will  evidently  exist  among  them 
by  means  of  which  they  may  be  eliminated.  So  long  as  we  are  dealing 
with  a  solution  of  a  single  electrolyte,  the  potential  may  obviously  be 
expressed  as  a  function  of  the  concentrations  of  the  ions  and  the  un-ion- 
ized  fraction;  that  is,  we  have: 


(106) 

Since  a  relation  exists  between  the  concentrations  C+,  C~  and  C  7  it  is 
obvious  that  one  of  these  variables  is  not  independent.  Since,  in  general, 
it  is  not  possible  to  determine  the  concentration  of  the  ions  and  of  the 
un-ionized  fraction  in  a  solution  of  an  electrolyte,  the  total  concentration 
of  the  salt  may  equally  well  be  employed  for  practical  purposes,  in  which 
case: 

(107) 


330       PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 


If  the  value  of  the  potential  sum  *2nM  may  be  experimentally  determined 
at  different  concentrations,  the  form  of  the  function  F(CS)  is  empirically 

known.  If  the  experimental  values  of  DnJlf  are  correct,  then  the  values 
of  F(CS),  as  determined  by  different  methods,  must  necessarily  be  in 

agreement.  This  result  has  been  verified  by  Lewis  and  Randall,10*  as 
we  shall  see  below.  When  mixtures  of  electrolytes  are  employed,  the 
expression  for  the  potential  obviously  becomes  a  function  of  a  greater 
number  of  variables.  In  the  case  of  a  salt  in  the  presence  of  another  salt 
with  a  common  ion,  the  potential  becomes  a  function  of  two  variables; 
and  in  that  of  a  salt  without  a  common  ion,  of  three  variables.  We 
should  not  expect,  therefore,  that  the  values  obtained  for  the  potential 
sum  in  mixtures  could  be  directly  compared  with  those  obtained  for  the 
same  electrolytes  in  a  pure  solvent.  The  methods  which  have  been 
adopted  by  investigators  in  this  field,  however,  have  consisted  essentially 
in  expressing  the  potential  of  an  electrolyte  in  a  mixture  as  a  function 
of  a  single  variable.  This  method  consists  in  introducing  a  variable 
defined  by  an  equation  of  the  form: 

(108)  Cm  =F(C1,  C2,...). 

This  function  is  given  such  a  form  that  the  value  derived  for  the  poten- 
tial sum  in  the  mixture,  on  introducing  Cm  as  variable,  corresponds  with 

that  of  a  solution  of  the  pure  substance  when  the  same  variable  is  intro- 
duced. If  such  a  function  exists,  then  we  are  led  to  conclude  that  the 
potential  sum  for  a  given  electrolyte  in  solution  is  dependent,  not  upon 
the  concentrations  of  the  various  substances  involved,  but  upon  some 
other  single  parameter. 

The  potential  of  an  electrolyte  as  a  function  of  its  concentration  may 
be  determined  directly  by  means  of  the  electromotive  force  of  concentra- 
tion cells.  More  indirectly,  the  potential  may  be  obtained  from  the 
vapor  pressures  of  these  solutions  and  from  other  related  properties,  such 
as  the  freezing  point,  boiling  point,  etc.  If  the  experimental  determina- 
tions are  correct,  the  values  of  the  potentials  derived  from  the  measure- 
ment of  these  different  properties  must  necessarily  be  in  agreement  with 
one  another. 

Lewis  and  Randall "  have  compared  the  available  experimental  data 
for  aqueous  solutions  in  this  way,  and  have  found  them  to  be  in  excellent 
agreement.  This  implies  the  correctness  of  the  methods  employed  in  cal- 
culating the  various  thermodynamic  quantities,  as  well  as  the  accuracy 

loa  Lewis  and  Randall,  J.  Am.  Chem.  Soc.  43,  1112   (1921). 
11  Idem,  loc.  cit. 


THEORIES  RELATING  TO  ELECTROLYTIC  SOLUTIONS          331 

of  the  experimental  methods,  by  means  of  which  the  data  were  secured. 
The  practical  application  of  thermodynamic  principles  to  electrolytic 
solutions  is  largely  due  to  G.  N.  Lewis.12  In  recent  years  numerous 
other  writers  have  occupied  themselves  with  this  subject.13  The  writers 
on  this  subject  have  commonly  employed  the  activity  function  of  Lewis,1* 
which  is  defined  by  the  equation: 

where  a  is  the  activity  and  io  is  a  function  independent  of  the  concentra- 
tion of  the  constituent  in  question.  The  ratio  of  the  activity  of  a  sub- 
stance to  its  concentration  is  termed  its  activity  coefficient  and  is  thus 
defined  by  tfie  equation: 

(110)  a=£. 

In  a  solution  of  an  electrolyte  we  have  an  equilibrium  of  the  type: 
n+AS  +  n-Az~  =  A', 

where  A'  represents  a  molecule  of  substance  which  dissociates  into  n+ 
positively  charged  ions  A^  and  ri~  negatively  charged  ions  A2~.  The 
number  of  charges  on  the  ions  is  not  indicated.  Introducing  the  values 
of  M  from  Equation  109  in  Equation  104  we  may  at  once  derive  the 
expression: 

(111)  log—          -  =K,  - 

au 

where  a+,  cr,  and  au  denote  the  activities  of  the  positive  and  negative 

ions  and  the  un-ionized  molecules,  respectively,  and  K  is  a  function  inde- 
pendent of  concentration.  For  the  change  in  the  potential  of  the  electro- 
lyte between  any  two  concentrations  of  the  system,  we  have  the  equa- 
tions: 

(112)  (2n'M')6—  (2n'M')a  =  RT  log  ^, 


ua 


(113)  (2nM)6  —  (2nM)a  =  RT  log 


"Lewis,  J.  Am.  Chem.  Soc.  S},  1631    (1912). 

"Bronsted,  J.  Am.  Chem.  Soc.  42,  761    (1920)  ;  Bjerrum,  Ztschr.  f.  Elektrochemie  24, 
321    (1918)  ;  Ztschr.  f.  Anorg.   Chem.   169,  275    (1920);   Harned,  J.  Am.    Chem.   Soc.   & 

loOo    (1920), 

„   oV«HVA?^roc-  Am-  Acad'  *3>  259  (1907)  ;  Zt8c*r-  /•  PhV*-  C^em.  61,  129  (1907)  ;  ibid., 
70,  — U   (1909). 


332       PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

From  Equation  112,  the  ratio  of  the  activities  of  the  un-ionized  mole- 
cules for  any  two  conditions  of  the  solution  may  be  determined  if  the 
potential  change  is  known.  Similarly,  the  ratio  of  the  activity  products 
of  the  ions  may  be  determined  from  Equation  113.  The  actual  value  of 
the  activity  product  is  not  in  general  determinable.  At  low  concentra- 
tions, however,  as  is  apparent  from  Equation  109,  the  activity  a  ap- 
proaches a  value  equal  to  that  of  the  concentration  C.  If  the  potential 
can  be  determined  at  sufficiently  low  concentrations,  that  is,  in  solutions 
sufficiently  dilute  so  that  the  laws  of  dilute  solutions  become  applicable, 
the  true  values  of  the  activity  products  may  be  determined.  In  systems 
in  which  a  reaction  takes  place  among  the  constituents  the  concentra- 
tions C  are  not  usually  determinable,  so  that  the  value  of  the  true  activity 
coefficients  a  remains  undetermined.  For  practical  purposes,  therefore,  a 
new  activity  coefficient  has  been  introduced,  defined  by  the  equation: 


where  Cs  is  the  total  concentration  of  the  electrolyte.    Further,  instead 

ol  employing  the  values  of  the  product  of  the  activity  coefficients,  some 
function  of  the  product  of  these  coefficients  is  employed  which  makes  the 
resulting  coefficient  more  nearly  comparable  with  that  of  a  solution  of  a 
single  molecular  species.  For  electrolytes,  Lewis  and  Randall  have  intro- 
duced a  coefficient  af)  defined  by  the  equation: 

1 


(115) 


where  af  and  Cr  may  be  called  the  reduced  activities  and  the  reduced 
concentrations  of  the  ions.15    In  a  solution  of  a  binary  electrolyte: 

15  The   nature   of  the  various   coefficients   may   be   further   elucidated   by   writing   the 
equations  for  the  potential  sum  in  somewhat  more  explicit  form.     We  have  : 


(117)  2nM  =  RT2n  log  C  +  Sni0  +  ZnJ, 
where 

ZnJ  =  RT  2tt  log  |. 

It  is  evident  that  this  equation  is  not  capable  of  being  employed  practically  as  an  inter- 
polation function,  since  C  is  not  determinable.     If,   now,   C"  is  replaced  by  C  gt  the  total 

salt  concentration  of  the  electrolyte  in  solution  in  pure  water, 

(118)  2nM  =  RT  2n  log  C8  +  2ni0  +  2nJa 

If  the  values   of  ZnM  are  known  for  different  values   of  C  ,  then  the   variation    in   the 
function     SwJg  over  the  concentrations  in  question  is  likewise  known.     In  Equation  117, 

"ZnJ  measures  the  change  in  the  value  of  the  potential  of  a  substance  in  a   real  system 
above  that  in  an  ideal  system  at  the  same  concentration.     When  the  reduced  concentration 


THEORIES  RELATING  TO  ELECTROLYTIC  SOLUTIONS 


333 


(116) 


ro+a-i 

t<VJ 


Numerical  Values.  In  comparing  the  thermodynamic  behavior  of 
different  electrolytes,  Lewis  and  Randall  have  compared  the  values  of  the 
reduced  activity  coefficients  ar  at  corresponding  concentrations.  In 

Table  CXXX  are  given  values  of  the  activity  coefficients  of  different 
electrolytes  at  a  number  of  concentrations.  These  values  have  been 

TABLE   CXXX. 

ACTIVITY  COEFFICIENTS  OF  VERY  DILUTE  AQUEOUS  SOLUTIONS  AT 
DIFFERENT  CONCENTRATIONS. 

0.01 
KC1,  NaCl  ...  0.922 

KN03   0.916 

KIOS,  NaI03  .  0.882 

K2S04  0.687 

H2S04 0.617 

BaCl2    0.716 

CoCl2    0.731 

MeS04  0.40(4) 

K3Fe(CN)6   ..  0.571 
La  (NO,).   ....  0.571 

derived  from  freezing  point  measurements  and  agree  well  with  those 
derived  by  other  methods.  In  Figure  59,  the  continuous  curve  represents 
the  values  of  the  activity  coefficients  of  sodium  chloride  at  different  con- 
centrations as  derived  from  freezing  point  determinations,  while  the 
points  indicated  by  circles  represent  values  of  the  coefficients  as  derived 

Gg  is  introduced,  Zfi«/g  measures  this  change  of  potential,  together  with  the  variation 
due  to  the  substitution  of  Cg  for  C.  If  we  write : 

2nJ     =  RT  Zn   log   a  „ 

o  o 

and  introduce  this  function  into  the  equation  for  the  activity,  we  have : 

RT  Zn  log  a  =  RTI.n  log  Cg  +  RT  Zn  log  erg, 
whence : 

Zn  log  ag  =  Zn  log^-- 

This  equation  defines  the  stoichiometric  activity  coefficient  of  Bronsted.  If  salts  were 
completely  ionized,  the  coefficient  ag  =a/Cg  would  be  a  measure  of  the  true  activity 
coefficient.  Since  potential  measurements  yield  values  of  the  activity  products  only,  an 
assumption  is  necessary  if  the  activity  coefficient  is  to  be  defined  by  means  of  an  equation 
of  the  form : 


0.005 

0.002 

0.001 

0.0005 

0.0002 

0.0001 

0.946 

0.967 

0.977 

0.984 

0.990 

0.993 

0.943 

0.965 

0.976 

0.984 

0.990 

0.994 

0.915 

0.946 

0.961 

0.972 

0.982 

0.988 

0.749 

0.814 

0.853 

0.885 

0.917 

0.935 

0.696 

0.782 

0.831 

0.871 

0.910 

0.932 

0.771 

0.830 

0.865 

0.894 

0.923 

0.939 

0.784 

0.840 

0.873 

0.900 

0.927 

0.943 

0.50 

0.61 

0.69 

0.75 

0.81 

0.85 

0.657 

0.752 

0.808 

0.853 

0.897 

0.922 

0.657 

0.752 

0.808 

0.853 

0.897 

0.922 

In  mixtures  of  any  number  of  electrolytes  the  definition  of  the  total  salt  concentration 
also  becomes  uncertain  and  a  further  assumption  of  an  arbitrary  nature  is  involved  in 
defining  the  activity  coefficients. 


334       PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 


from  electromotive  force  determinations.15*  It  is  evident  that  the 
activity  coefficients,  as  determined  by  the  two  methods,  are  in  remark- 
ably good  agreement.  This  indicates  the  correctness  of  the  methods  em- 
ployed in  the  calculations,  as  well  as  the  accuracy  of  the  experimental 
data.  Similar  calculations  have  been  made  for  aqueous  solutions  of 


0.5  1.0  1.5 

Square  Root  of  Concentration. 


2.0 


2,5 


FIG.  59. 


Activity  Coefficients  of  Sodium  Chloride  Solutions  as  a  Function  of 
Concentration. 


sulphuric  acid  by  the  freezing  point,  electromotive  force,  and  vapor  pres- 
sure methods.  Here,  again,  the  results  of  the  different  methods  have 
been  found  to  be  in  excellent  agreement.  In  Table  CXXXI  are  given 
values  of  the  activity  coefficients  of  typical  electrolytes  at  higher  con- 
centrations. 

TABLE   CXXXI. 


ACTIVITY  COEFFICIENTS  OF  TYPICAL  ELECTROLYTES. 


C=  0.01      0.02      0.05      0.1 

HC1(25°)  ....  0.924 
LiCl(25°)  ....  0.922 
NaCl(25°)  :..  0.922 

KC1(25°)    0.922 

KOH(25°)    ...  0.92 

KN03   0.916 

AgN03 0.902 

KI03,  NaI03  ..  0.882 

BaCl2 0.716 

CdCl2(25°)   ...  0.532 

K2S04  0.687 

H2S04(25°)  ...  0.617 
La(N03)3  ....  0.571 

MgS04    0.404 

CdS04    0.404 

CuS04    0.404 


0.894 

0.860 

0.814 

0.892 

0.843 

0.804 

0.892 

0.842 

0.798 

0.892 

0.840 

0.794 

0.89 

0.84 

0.80 

0.878 

0.806 

0.732 

0.857 

0.783 

0.723 

0.840 

0.765 

0.692 

0.655 

0.568 

0.501 

0.44 

0.30 

0.219 

0.614 

0.505 

0.421 

0.519 

0.397 

0.313 

0.491 

0.391 

0.326 

0.321 

0.225 

0.166 

0.324 

0.220 

0.160 

0.320 

0.216 

0.158 

0.2 

0.783 

0.774 

0.752 

0.749 

0.75 


0.5 

0.762 

0.754 

0.689 

0.682 

0.73 


1 

0.823 
0.776 
0.650 
0.634 
0.75 


3 

1.35 
1.20 
0.704 


0.655    0.526    0.396 


0.244 
0.271 
0.119 


0.178    0.150    1.70 


0.110    0.067 


and  Polack,  Jour.  Chem.  800.  U5t  1020   (1919), 


THEORIES  RELATING  TO  ELECTROLYTIC  SOLUTIONS          335 

As  may  be  seen  by  reference  to  Table  CXXX,  the  activity  coefficients 
of  electrolytes  of  the  same  type  do  not  differ  greatly  at  low  concentra- 
tions. The  activity  coefficient  increases  as  the  concentration  decreases 
at  low  concentrations.  In  solutions  of  strong  acids  and  bases  and  of  the 
alkali  metal  chlorides,  the  activity  coefficients  pass  through  a  minimum 
at  high  concentrations.  This,  however,  does  not  appear  to  be  a  general 
property  of  electrolytes,  since  silver  nitrate  does  not  exhibit  a  minimum 
up  to  concentrations  of  5  molal.  The  higher  the  type  of  salt,  the  more 
rapidly  does  the  activity  coefficient  decrease  with  increasing  concentra- 
tion. While,  as  a  rule,  salts  of  the  same  type  exhibit  the  same  values 
of  the  activity  coefficients,  a  number  of  exceptions  occur,  such  as  cadmium 
chloride,  whose  activity  coefficient  at  0.1  M  is  0.219,  while  that  of  barium 
chloride  at  the  same  concentration  is  0.50.  Aqueous  solutions  of  electro- 
lytes are  remarkable  for  the  uniformity  of  the  phenomena  presented. 
At  low  concentrations,  many  properties  of  these  solutions  differ  only  in- 
appreciably for  different  electrolytes  of  the  same  type.  The  same  rela- 
tion is  found  in  the  case  of  the  activity  coefficients.  At  higher  concen- 
trations, however,  different  electrolytes  exhibit  considerable  variations. 

At  low  concentrations,  the  values  of  the  reduced  activity  coefficients 

-fr-  approach  those  of  the  ionization  coefficient  y  =  T-.  The  significance 
cs  A° 

of  this  result  is  uncertain,  since,  even  at  the  lowest  concentrations,  aqueous 
solutions  of  strong  electrolytes  do  not  conform  to  the  requirements  of 
the  law  of  mass  action. 

A  comparison  of  the  activity  coefficients  of  solutions  of  pure  electro- 
lytes with  those  of  mixtures  cannot  be  effected  without  some  further 
assumption.  A  priori,  we  should  not  expect  the  activity  coefficient  of  a 
given  salt  in  a  mixture  of  electrolytes  to  correspond  closely  with  that 
in  a  solution  of  the  pure  substance.  From  Harned's  measurements  on 
the  electromotive  force  of  concentration  cells  with  mixe'd  electrolytes, 
Lewis  and  Randall  draw  the  conclusion  that  "in  any  dilute  solution  of  a 
mixture  of  strong  electrolytes,  of  the  same  valence  type,  the  activity 
coefficient  of  each  electrolyte  depends  solely  upon  the  total  concentra- 
tion." Where  the  mixture  contains  salts  of  different  valence  types,  they 
have  introduced  a  new  concentration  function  defined  by  the  equation: 

+... 

2 • 

where  Cs  is  the  total  molal  concentration  of  an  ionic  constituent  in  the 
solution  and  \j  is  the  number  of  charges  which  it  carries.  This  quantity, 


336        PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

C    ,  which  is  termed  the  ionic  strength,  is  employed  to  express  the  activity 

coefficient  of  a  salt  in  a  mixture  in  terms  of  a  single  variable.  From  their 
results  they  conclude  that  "in  dilute  solutions  the  activity  coefficient  of 
a  given  strong  electrolyte  is  the  same  in  all  solutions  of  the  same  ionic 
strength." 


75 


70 


65 


CO 


55 


50 


45 


40 


«  TIC1 

o  KNO3 

n  KC1 

x  HCI 

o  TIN03 

o  Ba  Cf2 

<?  T12S04 

6  K2S04 


0.0  0.1  0.2  0.3  0.4 

Square  Root  of  Ionic  Strength,  C 


0.5 


0.6 


FIG.   60.    Variation    of    l/Cr    for   Thallous   Chloride   as   a   Function    of   the    Ionic 

Strength,  C%. 


In  Figure  60  are  represented  values  of  the  reciprocal  of  the  mean 
molality  of  thallous  chloride,  defined  according  to  Equation  115,  against 
values  of  the  square  root  of  C  ,  defined  according  to  Equation  119.  In 

Table  CXXXII  are  given  values  of  the  activity  coefficients  of  thallous 
chloride  as  determined  from  solubility  experiments. 


THEORIES  RELATING  TO  ELECTROLYTIC  SOLUTIONS          337 

TABLE   CXXXII. 

ACTIVITY  COEFFICIENTS  OF  THALLOUS  CHLORIDE  IN  MIXTURES  AT  25°. 
Cm  InKN03  InKCl  InHCl  InTlNO3 

Tfl 

0.001  0.970  0.970  0.970  0.970 

0.002  0.962  0.962  0.962  0.962 

0.005  0.950  0.950  0.950  0.950 

0.01  0.909  0.909  0.909  0.909 

0.02  0.872  0.871  0.871  0.869 

0.05  0.809  0.797  0.798  0.784 

0.1  0.742  0.715  0.718  0.686 

0.2  0.676  0.613  0.630  0.546 

As  may  be  seen  from  the  figure,  the  curves,  connecting  the  reciprocal  of 
the  mean  reduced  concentration  -^-  with  the  ionic  strength,  diverge 

cr 

largely  at  higher  concentrations.  With  electrolytes  of  the  same  type, 
such  as  potassium  chloride  and  hydrochloric  acid,  the  divergence  is  not 
large.  With  potassium  nitrate,  however,  the  divergence  at  higher  con- 
centration is  marked,  as  is  also  that  for  the  ternary  electrolytes,  barium 
chloride,  thallous  sulphate,  and  potassium  sulphate.  In  view  of  the  fact 
that  these  curves  necessarily  pass  through  a  point  corresponding  to  a 
saturated  solution  of  pure  thallous  chloride,  the  conclusion  of  Lewis  and 
Randall  that  the  curves  become  coincident  at  lower  concentrations  is 
open  to  doubt,  for  it  is  conceivable  that,  since  the  curves  exhibit  a 
marked  curvature  at  higher  concentration,  such  curvature  may  be  main- 
tained in  mixtures  at  lower  concentration. 

Lewis  and  Randall  have  also  examined  the  solubility  curves  of  higher 
types  of  salts,  and  have  shown  that,  for  limited  concentration  intervals, 
their  principle  of  mixtures  is  able  to  account  for  the  observed  phenomena 
quite  closely. 

Solubility  Relations  According  to  Bronsted.  Bronsted16  has  also 
treated  the  solubility  relations  of  mixtures  of  electrolytes.16*  He  assumes 
that  the  van't  Hoff  factor  i  may  be  expressed  as  a  function  of  the  con- 
centration by  means  of  the  equation:  16b 

(120)  2  —  i 


"Bronsted,  loc.  cit. 

16«  Bronsted's  theory  of  the  solubility  effects  in  mixtures  of  electrolytes  is  simply 
interpreted  in  terms  of  Bjerrum's  theory  of  electrolytic  solutions.  Bjerrum  assumes  that 
electrolytes  are  completely  ionized  and  that  the  observed  effects  are  due  to  interaction 
between  the  ions.  So  far  as  the  experimental  foundation  of  Bjerrum's  theory  is  concerned, 
however,  it  is  based  chiefly  upon  observations  in  mixtures  of  electrolytes.  Naturally, 
Bjerrum's  theory,  in  the  case  of  a  solution  of  a  pure  electrolyte,  is  in  harmony  with  that 
of  Milner.  See  Bjerrum:  D.  Kgl.  Danske  Vidensk.  Selsk.  Skrifter  (7),  4,  1  (1906)  ;  Proc. 
7th  Intern.  Congr.  Appd.  Chem.,  Sect.  X  (1909)  ;  Ztschr.  f.  Electroch.  17,  392  (1911)  ;  'ibid., 
2Jf}  321  (1918). 

16bNoyes  and  Falk,  J.  Am.  Chem.  Soc.  32,  1011   (1910). 


338        PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

where  C  is  the  molal  concentration  and  x  is  a  constant  characteristic  of 
the  salt.  Combining  this  empirical  equation  with  the  differential  thermo- 
dynamic  equations  and  integrating,  he  obtains  the  equation: 

(  121  )  log  C+C~  =  2nC  j1/3  +  Const., 

where  C±  is  the  total  salt  concentration  of  the  saturated  solution.  In 
the  case  of  salts  without  a  common  ion,  Bronsted  assumes: 


where  Cs  is  the  total  concentration  of  the  saturating  salt.  This  leads  to 
the  equation: 

(122)  log^  =  x((y/»-C8>/»). 

V 

For  the  solubility  of  a  salt  in  a  mixture  containing  a  salt  with  a  common 
ion,  Bronsted  assumes: 

C"  =  C0     and    C"  =  C  ,, 

O  d 

where  C"  and  C"  are  the  concentrations  of  the  uncommon  and  the  com- 
mon ion  respectively.  This  leads  to  the  equation: 

csct 

(123)  log  jf+f  =  2*  (C(v»  -  C8W)  . 

so 

These  equations  express  the  solubility  of  the  saturating  salt  in  terms  of 
the  total  concentration  of  all  the  salts  in  solution.  The  value  of  the 
constant  K  depends  upon  the  type  of  salt.  For  uni-univalent  salts, 
x  =  approximately  1/3  ;  for  bi-bivalent  salts,  4/3  ;  and  for  tri-trivalent 
salts,  3.  Bronsted  shows,  in  the  first  place,  that  the  form  of  the  curve  is 
determined  by  the  values  of  the  constants  Cg  and  x.  In  the  presence  of 

salts  without  a  common  ion,  the  solubility  of  the  saturating  salt  is  in- 
creased due  to  addition  of  the  second  electrolyte;  and  this  increase  is  the 
greater,  the  greater  the  value  of  the  constant  >t.  Moreover,  the  relative 
increase  of  the  solubility  is  the  greater,  the  smaller  the  value  of  C0  .  In 

60 

the  presence  of  salts  with  a  common  ion,  the  form  of  the  solubility  curve 
depends  upon  the  number  of  charges  on  the  ions  and  the  number  of  ions 
resulting  from  the  different  salts.  Bronsted  shows  that  solubility  curves 
will,  in  general,  exhibit  a  minimum.  In  the  case  of  uni-univalent  salts, 
this  minimum  will  lie  at  very  high  jconcentrations  ;  for  bi-bivalent  salts, 
assuming  x  =  4/3,  the  minimum  concentration  is  0.12m;  and  for  tri- 


THEORIES  RELATING  TO  ELECTROLYTIC  SOLUTIONS          339 

trivalent  salts,  assuming  x  =  3,  the  minimum  is  at  0.01  m.  Bronsted's 
equations  therefore  account  for  the  solubility  relations  of  various  salts 
in  a  general  way,  including  the  minima  which  have  been  observed  in  the 
case  of  salts  of  higher  type.  Adjusting  the  value  of  the  constant  x  to 
represent  the  experimental  values  in  the  best  possible  manner,  Bronsted 
has  shown  that  his  equations  account  for  the  observed  solubilities  up  to 
0.1  N,  practically  within  the  limits  of  experimental  error. 

According  to  Bronsted's  equation,  the  activity  of  all  salts  ultimately 
passes  through  a  maximum.  Under  these  conditions,  the  solutions  will 
be  unstable  at  the  maximum  point  and  the  system  in  these  regions  should 
separate  into  two  liquid  phases.  In  the  case  of  salts  of  higher  type,  the 
concentration  at  which  this  phenomenon  should  occur  lies  in  regions 
where  the  concentration  is  fairly  low.  Bronsted  has  actually  been  able 
to  observe  separation  of  a  liquid  phase  in  solutions  of  salts  of  certain 
trivalent  ions. 

The  results  obtained,  on  comparing  the  thermodynamic  potential  of 
electrolytes  in  aqueous  solution,  show  that  these  values  as  derived  by 
different  methods  are  in  excellent  agreement.  Thermodynamic  principles 
alone  are  not  capable  of  supplying  information  as  to  the  nature  or  number 
of  the  molecular  species  present  in  electrolytic  solutions.  The  results  are 
naturally  in  agreement  with  the  assumption  that  electrolytes  are  com- 
pletely ionized  and,  in  view  of  the  fact  that  in  the  thermodynamic  treat- 
ment we  are  restricted  to  total  concentrations  and  not  to  actual  concen- 
trations, the  results  are  most  simply  interpreted  on  the  basis  of  this 
hypothesis.  This,  however,  does  not  preclude  the  possibility  that  un- 
ionized molecules  or  intermediate  ions  may  exist,  or,  indeed,  that  other 
complexes  may  be  present  in  these  solutions. 

3.  Theories  Taking  into  Account  the  Interionic  Forces,  a.  Theory 
of  Malmstrom  and  Kjellin.  A  great  many  investigators  have  attempted 
to  account  for  the  properties  of  solutions  of  electrolytes  by  taking  into 
account  the  forces  acting  between  the  charges.  According  to  this  view, 
as  was  pointed  out  by  Thomson 17  and  by  Nernst,17a  the  ionization  of  an 
electrolyte  under  given  conditions  should  be  the  greater  the  greater  the 
dielectric  constant  of  the  medium. 

Among  those  who  have  attempted  a  solution  of  the  problem  by  this 
method  are  Kjellin 18  and  Malmstrom.19  These  theories,  which  are  prac- 
tically the  same,  lead  to  an  equation  of  the  form: 

A  log  C{  =  log  £  +  log  Cu  + 

"Thomson,  Phil.  Mag.  [5],  S6t  320   (1893). 
"•Nernst,  Ztschr.  j.  pliya.  Chem.  13,  531   (1804). 
"Kjellin,  Ztschr.  f.  phys.  Chem.  77,  192   (1911). 

18  Malmstrom,  see  Kjellin,  above. 


340        PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

where  A,  B  and  K  are  constants  and  Cu  and  C^  are  the  concentrations  of 

the  ions  and  the  un-ionized  molecules,  respectively.  For  binary  electro- 
lytes A  has  a  value  of  approximately  1.5,  B  of  0.3  and  K  of  1.0.  Applied 
to  aqueous  solutions  of  sodium  and  potassium  chlorides,  this  equation 
was  found  to  reproduce  the  results  quite  closely  up  to  0.05  N,  the  con- 
stants of  the  equation  being  fitted  to  the  experimental  values.  Similar 
results  were  obtained  with  a  number  of  ternary  salts.  The  equation  is 
not  applicable  to  solutions  in  solvents  of  lower  dielectric  constant  such  as 
ammonia,  even  at  low  concentrations.  At  high  concentrations,  in  sol- 
vents of  dielectric  constant  less  than  20,  it  is  obviously  inapplicable, 
since,  according  to  this  equation,  A  necessarily  increases  with  concentra- 
tion. It  may  be  noted  that  the  form  of  this  equation  resembles  somewhat 
that  of  Bronsted's  for  the  solubility  of  a  salt  in  the  presence  of  other 
salts. 

b.  Theory  of  Ghosh.  The  most  comprehensive  theory  which  has 
been  proposed  to  account  for  the  behavior  of  solutions  of  electrolytes  is 
that  of  Ghosh.20  Ghosh  assumes  that  strong  electrolytes  are  completely 
ionized,  but  that  only  those  ions  whose  energy  is  sufficiently  great  to  over- 
come the  electrostatic  field  due  to  the  charges  are  active  in  carrying  the 
current.  It  is  difficult  to  see  how  Ghosh's  activity  coefficient  differs  from 
the  usual  ionization  coefficient.  Apparently,  what  this  author  has  in 
mind  is  that  the  ionic  complexes  persist  in  the  neutral  molecules.  While 
such  an  assumption  is  not  fundamental  to  the  older  ionic  theory,  it  is 
nevertheless  true  that  previous  investigators 21  in  this  field  have  long 
since  recognized  that  in  the  neutral  molecule  the  identity  of  the  ionic 
complexes  is  not  lost.  The  theory  of  Ghosh,  as  well  as  those  of  some 
other  writers,  would  be  more  readily  understandable  to  most  readers  if 
the  customary  nomenclature  had  been  retained. 

Ghosh  calculates  the  potential  due  to  the  field  on  the  assumption  that 
the  ions  are  distributed  in  the  medium  in  a  definite  manner  forming  a 
space  lattice.  He  assumes  that  the  space  lattice  of  a  salt  in  solution 
corresponds  to  that  of  the  salt  in  the  crystalline  state  and  therefrom  cal- 
culates the  distance  between  the  positive  and  negative  charges.  In 
calculating  the  potential,  Ghosh  assumes  that  the  ions  form  doublets  so 
that  the  work  involved  in  separating  the  ions  is  due  only  to  the  N  pairs 
of  positive  and  negative  ions.  This  theory  has  been  criticized  by  Part- 
ington,22  Chapman  and  George,23  and  more  recently  by  Kraus.24  These 

20 Ghosh,  Trans.  Chem.  Soc.  113,  449,  627,  707,  790  (1918). 

21  Noyes,  Aqueous  Solutions  at  High  Temperatures,  Carnegie  Publication  No,  63,  p.  350 
(1907) . 

22  Partington,  Trans.  Faraday  Soc.  15,  111   (1919-20). 

23  Chapman  and  George,  Phil.  Mag.  41,  799   (1921). 

"Kraus,  J.  Am.  Chem.  Soc.  W,  Dec.,   1921.  .....  .     .      , 


THEORIES  RELATING  TO  ELECTROLYTIC  SOLUTIONS 


341 


criticisms  need  not  be  further  considered  here  but  it  may  be  of  interest  to 
compare  the  conductance  values  calculated  according  to  Ghosh's  theory 
with  those  experimentally  determined. 

For  the  conductance  of  an  electrolytic  solution  Ghosh's  theory  leads 
to  the  following  equation: 


(124) 
where 
(125) 


log  A  =  log  AO  - 


DT 


2.3026  mR  ' 


Here  N  is  Avogadro's  number,  6.16  X  1023,  E  is  the  electrostatic  unit  of 
charge,  4.7  X  10~10  E.S.U.,  R  is  the  value  of  the  gas  constant  in  absolute 


,  Epichlorhydrin. 

0.0      0.0S 


0./S     0.20      O.25" 


2.16 
2.14- 


-'  2*0 


^2.06 

< 
be 
£ 


a.  oo 


1.96 


/.7B 
1.76 


/.  70 


A66   - 


/.**• 


/.62 


1.60 


0.+     0.6 


1-0        1.9. 

,  Water. 


FIG.  61.    Plot  of  Ghosh's  Conductance  Function  for  Solutions  of  Potassium  Chloride 
in  Water  at  18°  and  Tetraethylammonium  Iodide  in  Epichlorhydrin  at  25°. 

units,  and  m  is  a  factor  depending  upon  the  number  of  ions  n  resulting 
from  the  ionization  of  the  neutral  molecules  and  upon  the  number  of 
charges  associated  with  a  single  ion,  as  well  as  upon  the  manner  of  dis- 
tribution of  these  ions  in  the  solvent  medium.  It  is  evident  that,  for  a 


342       PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

given  solvent  at  a  given  temperature,  the  logarithm  of  the  equivalent  con- 
ductance is  a  linear  function  of  the  cube  root  of  the  concentration  and 
Ghosh's  theory  may  be  readily  tested  by  plotting  the  experimentally 
determined  values  of  log  A  against  those  of  C1/3.  If  the  equation  is 
applicable,  the  experimental  points  should  lie  upon  a  straight  line  from 
which  the  values  of  A0  and  p  may  be  determined.  If  the  equation  is  not 
applicable,  the  experimental  points  will  evidently  show  a  systematic 
deviation  from  a  straight  line. 

In  Figure  61  are  shown  the  curves  for  potassium  chloride  in  water  and 
for  tetraethylammonium  iodide  in  epichlorhydrin.  It  is  evident  from 
the  figure  that  the  experimental  points  lie  upon  a  curve  concave  toward 
the  axis  of  concentrations  at  low  concentrations  and  convex  toward  this 
axis  at  higher  concentrations,  with  an  inflection  point  between.  The 
experimental  points  show  a  systematic  deviation  from  a  linear  relation 
and  Ghosh's  equation  therefore  is  not  applicable.  In  Table  CXXXIII 
the  observed  and  calculated  conductance  values  are  compared. 

TABLE  CXXXIII. 

COMPARISON  OF  OBSERVED  AND  CALCULATED  VALUES  OF  A  FOR  KC1 
IN  WATER  AT  18°. 

A0=:  132.06    p==  3.620  X  103    !T=:291    D  =  81 
V  5X104    2X104       104      5X103   2X103       103       5X102 

Acaic     130.80     130.35     129.90    129.35     128.40     127.47     126.30 

Aobs'   129.51     129.32     129.00    128.70    128.04     127.27     126.24 

Aobs'-caic.        ...  —  1.39   —1.03   —0.90   —0.45   —0.36   —0.20  —0.06 

V  2X102      102  50          20         10          5  2        1 

ACaic     124.31     122.37     119.97     116.9     112.1     107.4      99.7    92.7 

Aob8     126.24     122.37     119.90    115.6     111.8     107.5     101.3    96.5 

Aobs,caic.       •  +0.03     ±0.00   —0.07   —0.3   —0.3   —0.1     +1.6  +3.8 

The  experimental  values  have  a  relative  precision  not  less  than  0.05 
per  cent.  It  is  evident,  from  the  table,  that  the  theoretical  values  deviate 
from  the  experimental  values  far  in  excess  of  any  conceivable  experimen- 
tal error,  except  at  a  few  points  in  the  immediate  neighborhood  of  the 
inflection  point,  which  is  at  about  0.01  normal.  As  may  be  seen  from 
the  curve  for  epichlorhydrin,  the  deviations  in  this  solvent  are  much 
greater  than  in  water.  It  is  to  be  noted,  too,  that  the  experimental  points 
again  lie  upon  a  curve  which  is  of  the  same  type  as  that  of  potassium 
chloride  in  water;  that  is,  the  curve  is  concave  toward  the  axis  of  concen- 
tration at  low  concentrations  and  convex  toward  this  axis  at  high  con- 


THEORIES  RELATING  TO  ELECTROLYTIC  SOLUTIONS          343 

centrations.  It  has  been  shown  that  this  form  of  the  curve  is  general  and 
that  in  solutions  of  non-aqueous  solvents  the  deviations  from  Ghosh's 
equation  are  much  greater  than  in  water,  and  therefore  are  far  in  excess 
of  any  possible  experimental  error.25 

Ghosh  has  likewise  treated  other  properties  of  electrolytic  solutions. 
In  view  of  the  fact  that  his  theory  fails  to  account  satisfactorily  for  the 
relation  between  the  conductance  and  the  concentration  of  electrolytic 
solutions,  it  is  unnecessary  to  consider  these  properties  here. 

c.  Milner's  Theory.  Of  the  various  theories  proposed  to  account  for 
the  properties  of  electrolytic  solutions,  that  of  Milner  is  perhaps  the  most 
noteworthy,  since  it  is  comparatively  free  from  arbitrary  assumptions. 
Milner 26  has  calculated  the  virial  for  a  system  of  positively  and  nega- 
tively charged  particles  by  statistical  methods,  and  therefrom  has  calcu- 
lated the  influence  of  the  ions  on  the  freezing  point  of  solutions.26*  He 
found,  in  effect,  that  the  virial  of  a  system  of  charged  particles  has  a 
finite  value,  from  which  the  osmotic  pressure  of  the  solution  may  be 
deduced,  and  therefrom  the  freezing  point. 

In  the  following  table  are  given  values  of  the  van't  Hoff  factor  i  for 
potassium  chloride  in  water  calculated  by  Milner,  together  with  the  values 
of  i  determined  by  Adams  directly  from  freezing  point  measurements. 

TABLE   CXXXIV. 

COMPARISON  OF  MILNER'S  VALUES  OP  i,  WITH  THOSE  EXPERIMENTALLY 

DETERMINED. 

C    0.005  0.01  0.02  0.05  0.1 

?:Milner 1.962  1.947  1.926  1.885  1.838 

*Adams 1.961  1.943  1.922  1.888  1.861 

As  may  be  seen  from  the  table,  the  calculated  values  of  i  are  in  excel- 
lent agreement  with  those  determined  by  Adams.  Milner's  values  are 
based  on  the  assumption  that  the  electrolyte  is  completely  ionized,  the 
observed  freezing  point  depression  being  due  entirely  to  the  interaction 
of  the  ions.  If  an  ionization  value  were  assumed  corresponding  to  that 
given  by  the  ratio  A/A0,  the  values  of  i,  as  calculated  by  Milner,  would 
be  lower  than  those  observed.  Milner  has  accordingly  suggested  that, 
within  these  ranges  of  concentration,  strong  electrolytes  are  completely 
ionized.  If  this  is  so,  the  change  in  the  conductance  of  electrolytes  must 

»Kraus,  loc.  cit. 

™  Milner,  Phil.  Mag.  23,  551   (1912)  ;  ibid.,  25,  742   (1913). 

*"»  Compare,  Cavanagh,  Phil.  Mag.  43,  606   (1922). 


344        PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

be  due  to  a  reduction  in  the  mean  carrying  capacities  of  the  ions  at  higher 
concentrations. 

Thus  far,  the  conductance  of  electrolytic  solutions  as  a  function  of 
their  concentration  has  not  been  accounted  for  with  equal  success.  Mil- 
ner 27  has  considered  this  problem,  but  without  arriving  at  an  expression 
for  the  conductance  as  a  function  of  concentration.  He  has  concluded, 
however,  that  the  decrease  of  conductance  at  low  concentration  must  be 
mainly  due  to  a  decrease  in  the  ionic  mobilities  and  not  to  a  decrease  in 
their  number.  The  argument  here  does  not  appear  to  be  altogether  con- 
vincing. Milner  assumes,  for  example,  that  the  undissociated  molecules 
are  normal  in  their  osmotic  behavior.  The  justification  for  this  assump- 
tion is  by  no  means  obvious.  Moreover,  experimental  facts  weigh  heavily 
against  the  generality  of  the  conclusion  reached.  Weak  electrolytes  in 
water,  and,  apparently,  all  classes  of  electrolytes  in  non-aqueous  solu- 
tions, approach  the  mass-action  law  as  a  limiting  form  at  low  concentra- 
tions. The  difficulty  is  not  alone  to  account  for  the  failure  of  the  mass- 
action  law  in  solutions  of  strong  electrolytes  in  water  but,  also,  to  account 
for  the  applicability  of  this  law  to  solutions  in  other  solvents  where,  judg- 
ing by  the  lower  value  of  the  dielectric  constant,  the  interionic  forces  are 
much  greater  than  in  water.  Furthermore,  according  to  Milner 's  theory, 
different  electrolytes  in  dilute  solutions  should  exhibit  practically  identi- 
cal properties  both  as  regards  their  osmotic  and  their  electrical  properties. 
This  condition  is  approximately  fulfilled  in  water,  but  not  in  solutions  in 
non-aqueous  solvents.  In  these  latter  solvents,  the  electrolyte  appears 
to  retain  its  individuality  even  at  exceedingly  low  concentrations.  Any 
theory  which  cannot  give  an  account  of  this  fundamental  property  of 
electrolytic  solutions  is  obviously  incomplete. 

It  is  not  difficult  to  see  in  what  manner  the  conductance  would  be 
influenced  by  interionic  action  at  higher  concentrations.  According  to 
Milner,  the  ions  are  not  distributed  haphazard  throughout  the  medium, 
but,  on  the  average,  as  the  result  of  interaction  between  the  charges,  ions 
having  like  charges  are  somewhat  farther  apart  and  ions  having  unlike 
charges  somewhat  nearer  together  than  would  otherwise  be  the  case. 
Ordinarily  it  is  assumed  that  a  charged  particle  moves  in  a  uniform 
electric  field.  If,  however,  the  ions  are  combining  and  dissociating,  or, 
in  any  case,  if  charged  particles  approach  each  other  sufficiently  closely, 
the  surrounding  field  will  be  influenced  and  the  speed  of  the  ions  will  vary 
for  different  individuals,  depending  upon  the  proximity  of  other  ions. 

According  to  this  view,  the  ratio  y  =  -*-  is  a  measure,  not  of  the  number 

-     A0 

"Milner,  PUl.  Mag.  S5,  214  and  352   (1918). 


THEORIES  RELATING  TO  ELECTROLYTIC  SOLUTIONS          345 

of  particles  actually  engaged  in  the  transport  of  the  current,  but  of  the 
mean  conducting  power  of  the  ions.  It  does  not  necessarily  follow,  how- 
ever, according  to  this  view,  that  all  the  ions  in  solution  are  at  all  times 
acting  as  carriers  of  the  current. 

Lewis  and  Randall 28  have  recently  pointed  out  that  the  ionization  of 
an  electrolyte  cannot  be  defined  without  some  degree  of  arbitrariness. 
This  difficulty  is  not  one  confined  to  electrolytic  solutions.  In  all  sys- 
tems, in  which  reaction  takes  place  among  a  number  of  constituents 
throughout  the  mass  of  the  mixture,  the  definition  of  the  concentration 
of  the  various  constituents  concerned  becomes  uncertain.  So  long  as  the 
system  is  dilute,  the  concept  of  concentration  is  definite;  but,  when  the 
concentrations  reach  such  values  that  the  forces  acting  between  the  con- 
stituents become  appreciable,  the  concept  embodied  in  the  term  molecule 
becomes  indistinct.  This  difficulty  arises  of  necessity  whenever  we  pass 
from  the  purely  thermodynamic  to  the  kinetic  method  of  treating  systems 
of  real  substances.  That  these  various  difficulties  should  arise  in  solu- 
tions of  electrolytes  is  not  surprising,  since  these  are  the  only  concentrated 
systems  regarding  which  we  have  data  sufficiently  accurate  to  enable  us 
to  observe  the  deviations  from  ideal  systems  with  any  considerable  degree 
of  certainty.  That  un-ionized  molecules  exist  in  aqueous  solutions  of 
ternary  salts  in  water  appears  to  be  conclusively  demonstrated  by  the 
fact  that  transference  measurements  have  shown  that  complex  cations 
exist.  Thus,  the  transference  number  of  the  cadmium  ion,  in  cadmium 
iodide,  according  to  Hittorff,  is  greater  than  unity  at  high  concentrations, 
and  the  manner  in  which  the  transference  number  of  cadmium  chloride 
varies  with  the  concentration  indicates  that  its  behavior  is  not  essentially 
different  from  that  of  cadmium  iodide.  It  must  be  assumed,  therefore, 
that,  in  solutions  of  cadmium  salts,  ions  of  the  type  CdX>  exist.  If  this 
is  true  of  one  electrolyte,  the  same  may  well  be  true  of  others. 

Finally,  it  is  not  sufficient  that  a  theory  of  electrolytic  solutions  shall 
account  merely  for  a  diminution  in  the  conducting  power  of  electrolytes 
with  increasing  concentration,  for,  in  solutions  in  non-aqueous  solvents, 
the  conductance  increases  with  increasing  concentration  at  higher  con- 
centrations; and,  if  the  dielectric  constant  is  sufficiently  low,  the  con- 
ductance increases  with  increasing  concentration  even  at  relatively  low 
concentrations. 

d.  Hertz's  Theory  of  Electrolytic  Conduction.  P.  Hertz  29  has  at- 
tempted to  solve  the  problem  of  electrolytic  conduction  by  taking  into 
account  the  interionic  forces.  He  has  derived  the  following  equation 

*Loc.  cit. 

»  Hertz,  Ann.  d,  Phya.  37,  1   (1911). 


346       PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

expressing  the  relation  between  the  equivalent  conductance  A  and  the 
concentration  C  of  the  solution: 

(126) 

where 

u 
(127)  Si(u)  = 


u 


(128)  Ci(u)  =  j  ^^  du, 


(129)  ip(M)=B(Ao  —  A), 
and 

(130)  u 


Here  A0,  A  and  £  are  constants.  A0  is  the  limiting  value  which  the 
equivalent  conductance  approaches  as  the  concentration  decreases  indefi- 
nitely. This  equation  is  of  the  form: 

(131)  £(A0  —  A)  nrtpkiC1/8). 

It  is  evident  that,  for  a  given  solvent  under  given  conditions,  the 
conductance  function  will  have  the  same  form  for  different  electrolytes 
according  to  this  theory.  If  the  values  of  ip  (u)  and  of  u  are  represented 
graphically,  then  it  should  be  possible  to  transform  the  curve  for  one 
electrolyte  into  that  for  another  by  merely  altering  the  scale  of  plotting. 
It  is  obvious  that  this  condition  will  be  very  nearly  fulfilled  in  aqueous 
solutions  of  strong  binary  electrolytes,  since  the  ionization  of  different 
electrolytes  at  lower  concentrations  is  practically  identical.  If  Hertz's 
theory  held  strictly,  the  value  of  the  constant  A  would  be  predetermined 
by  the  nature  and  condition  of  the  solvent  and  would  be  independent  of 
the  nature  of  the  electrolyte.  The  difference  in  the  values  of  the  con- 
ductance of  different  electrolytes,  therefore,  would  be  accounted  for  by  a 
difference  in  the  values  of  the  constants  A0  and  B,  and  the  different  con- 
ductance curves  should  be  transformable  one  into  the  other  by  merely 
altering  the  values  of  these  constants;  or,  if  A0  is  otherwise  determined, 
by  merely  altering  the  value  of  the  constant  B. 


THEORIES  RELATING  TO  ELECTROLYTIC  SOLUTIONS          347 

Lorenz  30  has  tested  the  applicability  of  Hertz's  function  to  aqueous 
solutions  of  binary  electrolytes  and  has  concluded  that  this  function  is 
applicable.  As  has  just  been  pointed  out,  this  was  to  have  been  expected. 
It  should  be  noted,  however,  that  the  value  of  A,  according  to  Lorenz, 
differs  appreciably  for  different  electrolytes.  This  result  may,  in  part, 
be  due  to  the  fact  that  the  function  has  been  applied  at  concentrations 
where  the  viscosity  effects  become  appreciable. 

It  is  evident  that  Hertz's  function  will  not  be  generally  applicable 
to  solutions  in  non-aqueous  solvents,  certainly  not  unless  the  value  of 
A  is  assumed  to  differ  largely  for  different  electrolytes.  Furthermore,  it 
will  be  entirely  inapplicable  to  solutions  in  non-aqueous  solvents  of  low 
dielectric  constant  at  higher  concentrations.  It  is  evident  from  Equation 
126  that  the  factor  of  u3  is  essentially  positive  so  that  A0  —  A  must 
necessarily  increase  with  increasing  concentration.  It  is  known,  however, 
that,  in  solvents  of  low  dielectric  constant,  the  value  of  A  passes  through 
a  minimum,  after  which  the  value  of  A0  —  A  decreases  with  increasing 
concentration.  This  theory,  like  others  of  its  kind,  is  at  best  restricted 
in  its  applicability.  As  yet  it  has  not  been  compared  with  experimental 
data  in  a  sufficient  number  of  solutions  to  make  it  possible  to  form  a 
clear  opinion  as  to  the  range  of  its  applicability.  In  any  case,  it  is  in- 
applicable to  solutions  in  solvents  of  very  low  dielectric  constant,  even 
though  these  solutions  may  be  dilute.  Here  again,  as  in  the  case  of 
Milner's  theory,  the  difference  in  the  behavior  of  strong  and  weak  elec- 
trolytes remains  to  be  accounted  for. 

4.  Miscellaneous  Theories.  A  great  many  other  theories  have  been 
suggested  to  account  for  the  behavior  of  electrolytic  solutions.  In  gen- 
eral, these  theories  have  not  been  worked  out  sufficiently  to  comprehend 
within  their  scope  more  than  a  limited  number  of  properties  of  a  limited 
number  of  systems.  Many  of  them,  indeed,  are  purely  qualitative  in 
character. 

To  account  for  the  increase  in  the  conductance  of  solutions  of  elec- 
trolytes in  solvents  of  very  low  dielectric  constant,  Steele,  Macintosh 
and  Archibald  31  have  suggested  that  at  higher  concentrations  the  elec- 
trolyte polymerizes,  and  that  only  these  polymerized  molecules  are  capa- 
ble of  ionization.  They  show  that,  if  a  sufficient  degree  of  polymerization 
is  assumed,  an  ionization  curve  is  obtained  somewhat  similar  in  form  to 
that  of  ordinary  electrolytes  in  aqueous  solution.  Thus  far,  this  theory 
is  purely  qualitative  in  character  and  an  exact  test  of  its  applicability 
is  therefore  not  possible.  We  should  expect,  however,  that  if  only 

10  Lorenz  and  Michael,  Ztschr.  /.  anorg.  Chem.  116.  161  (1921):  Lorenz  and  Neu. 
ibid.,  116,  45  (1921)  ;  Lorenz  and  Osswald,  ibid.,  114,  209  (1920). 

"Steele,  Macintosh  and  Archibald,  Phil.  Trans.  [A]  205,  99   (1905). 


348       PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

polymerized  molecules  were  capable  of  ionization,  intermediate  ions 
would  be  present  in  solution  and  transference  measurements  with  such 
solutions,  therefore,  should  yield  very  abnormal  values  for  the  transfer- 
ence numbers.  While  certain  transference  numbers  are  unquestionably 
abnormal  and  while  it  is  indeed  very  probable  that  polymerization  often 
occurs  in  solutions  of  electrolytes  in  solvents  of  both  high  and  low  dielec- 
tric constant,  it  remains  to  be  shown  that  the  phenomenon  is  a  general 
one  and  that  it  is  capable  of  accounting  for  the  observed  properties  of 
electrolytic  solutions.  Nevertheless,  it  is  highly  probable  that  the  effect 
of  polymerization  will  have  to  be  taken  into  account  in  many  cases  at 
higher  concentrations.  It  appears,  however,  that  polymerization  should 
lead  to  a  lower  rather  than  to  a  higher  value  of  the  conductance.  Trans- 
ference measurements  with  the  alkali  metal  halides  in  acetone  yield 
abnormally  high  values  for  the  cations,  indicating  the  formation  of  a 
complex  cation.  It  is  to  be  noted,  however,  that  the  conductance  of  the 
halide  is  the  lower  the  greater  its  tendency  to  form  complexes.  Thus,  the 
conductance  of  lithium  chloride  in  acetone  at  higher  concentrations  is 
much  lower  than  that  of  potassium  iodide  or  sodium  iodide.  That  com- 
plex ions  are  formed  in  solutions  of  cadmium  iodide  in  water  was  shown 
by  Hittorf,  as  has  already  been  pointed  out.  The  assumed  ionization 
process  in  solutions  of  electrolytes  is  in  a  large  measure  hypothetical. 
This  may  account  for  numerous  discrepancies  at  higher  concentrations. 

Other  writers  consider  solutions  of  strong  electrolytes  to  be  similar 
to  solutions  of  colloids.  Among  these  are  Reychler,32  Georgievics  33  and 
Wo.  Ostwald.34  These  theories,  however,  appear  to  be  little  more  than 
analogous,  based  chiefly  upon  the  similarity  between  the  Storch  equation 
and  the  adsorption  equation.  The  Storch  equation  is  only  an  approxima- 
tion in  aqueous  solutions  which,  in  other  solvents,  fails  entirely.  The 
osmotic  effects  in  solutions  of  electrolytes,  also,  are  not  in  harmony  with 
the  view  that  solutions  of  strong  electrolytes  are  colloidal  in  character. 

Some  writers  attempt  to  account  for  the  properties  of  aqueous  solu- 
tions by  taking  into  account  reactions  between  the  solvent  and  the  elec- 
trolyte. In  this  connection,  it  is  to  be  noted  that  electrolytic  solutions  are 
not  confined  to  solvents  of  the  water  type.  Indeed,  such  solvents  need 
not  necessarily  contain  hydrogen  and,  in  fact,  may  be  elementary  sub- 
stances, or  neutral  carbon  compounds  such  as  chloroform.  In  view  of 
this  fact,  it  is  highly  improbable  that  the  properties  of  electrolytic  solu- 
tions may  be  generally  accounted  for  on  the  basis  of  chemical  processes 

82  Reychler,  "Etude  sur  1'Equilibre  de  Dissociation,"  Brochure  No.  3,  Bruxelles  (1917), 

83  Georgievics,  Ztschr.  f.  pJiys.  Chem.  90,  356  (1915). 
"Ostwald,  Ztschr.  Ctiem.  Ind.  Roll.  9,  189   (1911). 


THEORIES  RELATING  TO  ELECTROLYTIC  SOLUTIONS          349 

taking  place  between  the  solvent  and  the  dissolved  electrolyte.  But 
here,  again,  there  are  doubtless  many  instances  where  interaction  between 
the  electrolyte  and  the  solvent  or  an  added  non-electrolyte  is  a  primary 
factor  in  the  ionization  process,  particularly  at  higher  concentrations. 

5.  Recapitulation.  In  recapitulation,  solutions  of  strong  electro- 
lytes, even  at  low  concentrations,  do  not  conform  to  the  laws  of  dilute 
systems.  The  thermodynamic  properties  of  these  solutions  can  not, 
therefore,  be  employed  for  the  purpose  of  determining  the  state  of  the 
electrolyte  in  these  solutions.  The  conductance  method  might  be  ex- 
pected to  give  a  measure  of  the  fraction  of  the  ionized  and  un-ionized 
molecules  present.  However,  the  fact  that  the  relative  conductance  of 
the  ions  of  strong  acids  varies  at  low  concentrations  renders  the  results 
of  the  conductance  method  doubtful. 

The  hypothesis  that  electrolytes  are  completely  ionized  up  to  fairly 
high  concentrations  lacks  experimental  support.  The  agreement  of  the 
hypothesis  with  the  consequences  of  thermodynamic  principles  can  not 
be  looked  upon  as  lending  material  support,  since  thermodynamics  can 
teach  us  nothing  with  regard  to  the  molecular  state  of  a  system  without 
a  supplementary  hypothesis  which  directly  or  indirectly  involves  the 
equation  of  state.  The  fact  that  the  law  of  mass-action  is  approached 
as  a  limiting  form  in  aqueous  solutions  of  weak  electrolytes  and  in  non- 
aqueous  solutions  of  all  electrolytes  for  which  reliable  data  are  available 
indicates  that,  if  strong  electrolytes  in  aqueous  solution  are  completely 
ionized,  this  constitutes  only  a  particular  case  and  the  general  problem 
still  remains  to  be  solved. 

Any  theory  which  undertakes  to  account  for  the  decreased  conduct- 
ance of  electrolytes  at  higher  concentrations,  on  the  assumption  that  the 
conductance  change  is  due  to  a  change  in  the  speed  of  the  ions,  must 
likewise  account  for  the  fact  that,  in  solvents  of  low  dielectric  constant, 
the  conductance  passes  through  a  minimum  value  after  which  it  increases. 
This  point  may  lie  at  relatively  low  concentrations. 

The  theories  of  electrolytic  solutions  thus  far  advanced  are  founded 
chiefly  on  observations  relating  to  aqueous  solutions.  There  is  great 
danger,  here,  that  phenomena  may  be  assumed  as  general  which,  in  fact, 
are  only  particular.  It  is  of  the  greatest  importance  to  analyze  the 
results  obtained  from  a  study  of  the  properties  of  solutions  in  various  sol- 
vents in  order  to  determine  which  of  these  are  general,  applying  to  all 
electrolytic  solutions,  and  which  are  particular,  applying  only  to  solutions 
in  certain  solvents  or  under  certain  conditions.  Aqueous  solutions  are 
characterized  by  the  uniformity  of  the  phenomena  presented  by  different 
electrolytes.  In  other  words,  the  electrolyte,  in  aqueous  solution,  has, 


350       PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

in  a  large  measure,  lost  its  individuality.  This  is  not  true  of  solutions 
in  other  solvents.  Here  the  electrolyte  retains  its  individual  character- 
istics even  at  very  low  concentrations.  It  is  interesting  to  note  that,  at 
higher  temperatures,  certain  of  the  individual  properties  of  electrolytes 
in  aqueous  solution  disappear  while  others  make  their  appearance.  Thus, 
the  ionic  conductances  approach  one  another  at  higher  temperatures, 
while  the  ionizatibn  values  diverge  the  more  the  higher  the  temperature. 
It  is  not  to  be  doubted  that  the  properties  of  aqueous  solutions  at  higher 
temperatures  closely  resemble  those  of  non-aqueous  solutions  under 
ordinary  conditions. 

It  is  not  unlikely  that,  in  the  end,  many  of  the  theories,  which  have 
been  suggested  from  time  to  time  and  found  inapplicable,  contain  certain 
elements  of  truth.  The  error  has  been  introduced  in  attempting  to  apply, 
generally,  theories  which  are  applicable  only  to  special  cases.  It  appears 
probable  that,  ultimately,  it  will  be  necessary  to  take  into  account,  under 
various  conditions,  a  change  in  the  speed  of  the  ions  with  concentration  as 
well  as  a  change  in  the  degree  of  ionization.  At  the  same  time  there  will 
doubtless  be  found  many  cases  in  which  intermediate  ions  are  formed  and 
in  which  the  electrolyte  polymerizes.  Yet  there  is  found,  in  all  electro- 
lytic solutions,  a  certain  unity  among  the  phenomena,  which  indicates 
the  existence  of  a  comparatively  small  number  of  chief  governing  factors. 


Chapter  XIII. 
Pure  Substances,  Fused  Salts,  and  Solid  Electrolytes 

1.  Substances  Having  a  Low  Conducting  Power.  In  the  preceding 
chapters,  the  properties  of  solutions  of  electrolytes  have  been  discussed. 
We  shall  now  consider,  briefly,  the  properties  of  pure  substances  in  the 
liquid  state.  Nearly  all  substances  in  the  fused  condition  exhibit  a 
measurable,  though  often  small,  conducting  power  for  the  electric  cur- 
rent. Even  such  substances  which  we  ordinarily  class  as  insulators  con- 
duct the  current  in  some  degree.  What  the  nature  of  the  conduction 
process  is  in  these  substances  has  not  been  shown,  but  in  all  likelihood 
the  process  is  an  ionic  one;  that  is,  the  current  is  carried  by  particles  of 
atomic  or  molecular  dimensions.  A  typical  example  of  this  class  of  con- 
ductors, or  perhaps  more  properly  insulators,  is  found  in  the  hydrocar- 
bons. It  has  been  shown  that  the  conductance  of  substances  of  this  type 
is  materially  affected  by  the  presence  of  small  amounts  of  impurities. 
The  specific  conductance  of  nearly  all  poorly  conducting  substances  is 
materially  decreased  by  careful  drying  and  fractionation.  Evidently, 
therefore,  in  part  at  least,  the  conductance  of  this  class  of  substances  is 
due  to  the  presence  of  other  substances,  as  a  result  of  which  their  con- 
ductance is  materially  increased.  We  have,  however,  no  knowledge  of 
the  nature  of  the  charged  particles  by  means  of  which  conduction  is 
effected.  * 

In  the  case  of  petroleum  ether  and  hexane,  it  has  been  found  possible 
to  carry  the  process  of  purification  so  far  that  the  effect  of  impurities  is 
almost  entirely  eliminated.  It  has  been  found  that  the  residual  con- 
ductance in  these  solvents  is  chiefly  due  to  the  action  of  radiations  from 
surrounding  bodies,  as  a  result  of  which  the  solvent  itself  is  ionized.1 
The  conductance  under  these  conditions  was  found  to  be  altered  by  sur- 
rounding the  conductance  vessel  with  screens  which  absorb  the  external 
radiation.  The  conductance  of  pure  hexane,  therefore,  is  lower  than  that 
due  to  the  ions  produced  by  the  radiation  from  surrounding  bodies  and 
it  is  possible  that  the  conductance  of  this  substance  is  in  effect  zero. 
Under  ordinary  conditions,  the  conductance  of  the  hydrocarbons  is  due 
primarily  to  impurities. 

*Jaff6,  Ann.  d.  Phys.  32,  148   (1910). 

351 


352        PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

Recent  investigations  on  the  conduction  process  in  solid  dielectrics 
have  disclosed  the  fact  that  in  these  media  Ohm's  law  is  not  obeyed.2 
The  substances  investigated  were  mica,  glass,  paraffin,  shellac  and  cellu- 
loid. Excepting  paraffin,  for  which  the  conductance  was  so  low  that  the 
results  were  uncertain,  the  conductance  was  found  to  increase  with  the 
applied  potential.  The  logarithm  of  the  specific  conductance  increases 
approximately  as  a  linear  function  of  the  potential  gradient.  In  the  case 
of  mica,  with  which  substance  measurements  were  made  over  a  large 
range  of  potential,  the  conductance  curves  are  slightly  concave  toward  the 
axis  of  potentials.  In  the  case  of  glass  the  conductance  increase  at  higher 
temperatures  was  found  to  be  noticeably  smaller  than  at  lower  tempera- 
tures. 

Since  Ohm's  law  does  not  hold,  it  must  be  assumed  either  that  the 
number  of  carriers  increases  with  the  applied  potential  or  that  the  mean 
speed  of  the  carriers  increases.  It  is  not  improbable  that,  under  the 
action  of  the  applied  potential,  carriers  of  a  type  differing  from  those 
normally  present  in  the  dielectric  medium  may  be  formed.  It  is  of  par- 
ticular interest  to  note  that  in  glass,  which  is  an  electrolyte  at  higher 
temperatures,  the  above  mentioned  results  indicate  a  conduction  process 
differing  from  that  at  higher  temperatures. 

Compounds  of  hydrogen  with  elements  which  are  strongly  electro- 
negative are  in  general  ionized  to  a  slight  degree.  The  most  familiar 
example  of  this  type  is  water  itself,  which  in  the  pure  state  has  a  specific 
conductance  in  the  neighborhood  of  0.042  X  10~7.2a  Other  hydrogen  de- 
rivatives of  strongly  electronegative  groups  likewise  appear  to  conduct 
the  current  in  the  pure  state,  some  of  them  much  more  readily  than 
water.  The  specific  conductance  of  formic  acid  appears  to  lie  in  the 
neighborhood  of  10~5.  In  these  cases,  however,  the  process  of  purification 
has  not  been  carried  to  such  a  point  that  it  can  with  certainty  be  stated 
that  the  residual  conductance  is  entirely  or  chiefly  due  to  the  ionization 
of  the  solvent  alone.  In  the  case  of  hydrogen  derivatives,  in  which  the 
hydrogen  is  not  joined  to  a  strongly  electronegative  group,  the  residual 
specific  conductance  is  as  a  rule  relatively  low  and  it  is  as  yet  uncertain 
to  what  the  residual  conductance  is  due.  Acetone,  for  example,  may  be 
purified  to  a  point  where  its  specific  conductance  is  of  the  order  of  10~8, 
but  whether  this  residual  conductance  is  due  to  acetone  itself  or  to  some 
impurity  is  unknown.  The  same  obviously  holds  true  of  solvents  which 
contain  no  hydrogen,  such  as  sulphur  dioxide,  bromine,  etc. 

The  hydrogen  derivatives  of  the  strongly  electronegative  groups  are 

3Poole,  PUl.  Mag.  42,  488  (1921). 

"Kohlrausch  and  Heydweiller,  Ann.  d.  Phys.  83,  209  (1894). 


PURE  SUBSTANCES,  FUSED  SALTS,  SOLID  ELECTROLYTES      353 

perhaps  to  be  classed  as  salts.  In  other  words,  these  compounds  should 
be  classed,  not  with  the  ordinary  hydrocarbons,  but  rather  with  the  dis- 
tinctly salt-like  substances.  These  derivatives,  when  dissolved  in  water, 
or  other  suitable  solvents,  yield  solutions  which  conduct  the  current  with 
great  facility  and  which  often  form  compounds  with  the  solvent.  Hydro- 
chloric acid  forms  a  stable  complex,  ammonium  chloride,  with  ammonia; 
and  with  water  at  low  temperature  it  has  been  shown  to  form  a  complex 
HC1.H20.3  In  water  itself,  therefore,  hydrogen  and  hydroxyl  ions  do 
not  consist  merely  of  a  hydrogen  atom  and  an  OH  group  associated  with 
the  positive  and  negative  charge  respectively,  but  rather  of  complexes  in 
which  the  solvent  itself  is  involved.  In  a  sense,  therefore,  water  and 
ammonia  and  hydrogen  chloride  may  be  considered  to  be  related  to  salts. 
However,  the  typical  salts  in  a  fused  state  exhibit  in  most  instances  a 
conductance  much  greater  than  that  of  the  substances  which  we  have 
just  been  discussing. 

With  a  few  exceptions,  fused  salts  conduct  the  current  with  extreme 
facility.  Among  these  exceptions  mercuric  chloride  is  one  of  the  most 
common  and  striking  examples.  This  salt  is  itself  an  electrolytic  solvent 
for  other  salts,  while  its  specific  conductance  in  the  pure  state  is  very 
low.*  Correspondingly,  solutions  of  mercuric  chloride  in  other  solvents, 
as  for  example  water,  appear  to  be  only  slightly  ionized.  This  class  in- 
cludes the  organic  tin  salts  of  the  type  R3SnX.  Trimethyltin  iodide,  for 
example,  is  a  liquid  at  ordinary  temperatures  whose  conductance  is  less 
than  4  X  10~5.  This  salt  when  dissolved  in  water  is  ionized  nor- 
mally.5 

2.  Fused  Salts.  Inorganic  substances  which  are  non-electrolytes  in 
solution,  in  general,  possess  only  a  very  low  conducting  power  in  the  pure 
state.  This,  for  example,  is  the  case  with  boric  oxide.  On  the  other 
hand,  oxides  of  the  strongly  electropositive  elements  appear  to  be  con- 
ductors in  the  fused  or  even  in  the  solid  state.  It  is,  however,  the  typical 
salts  in  their  fused  state  which  are  of  greatest  interest.  These  substances, 
in  general,  conduct  the  current  with  extreme  facility,  by  means  of  a 
purely  ionic  process,  since,  as  has  been  shown,  Faraday's  law  applies. 

In  Table  CXXXV  are  given  values  of  the  specific  conductance  \i  of 
sodium  nitrate  at  different  temperatures,  together  with  the  equivalent 
conductance  A  as  calculated  from  the  known  specific  volume,  the  fluidity 

of  the  fused  salt  F,  and  the  ratio  of  the  conductance  to  the  fluidity  ^ .6 

JT 

'Rupert,  J.  Am.  Chem.  Soc.  SI,  851   (1909). 

•Foote  and  Martin,  Am.  Chem.  J.  41,  45   (1909). 

8  Unpublished  observations  by  Mr.  C.  C.  Callis  in  the  Author's  Laboratory: 

•Goodwin  and  Mailey,  Phys.  Rev.  25,  469   (1907)  ;  t&id.,  26,  28   (1908). 


354        PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

TABLE  CXXXV. 

CONDUCTANCE  AND  FLUIDITY  OF  SODIUM  NITRATE  AT  DIFFERENT 
TEMPERATURES. 

t  [i  A  F  K/F 

350°  1.173  52.87  42.6  1.24 

400  1.384  63.59  54.0  1.18 

450  1.562  73.15  65.0  1.12 

500  1.716  81.94  77.2  1.06 

It  will  be  observed  that  the  specific  conductance  \i,  as  well  as  the  equiva- 
lent conductance  A,  increases  very  nearly  as  a  linear  function  of  the  tem- 
perature. Obviously,  the  equivalent  conductance  will  vary  nearly  in 
proportion  to  the  specific  conductance,  since  the  density  of  the  fused  salt 
varies  only  comparatively  little  with  temperature.  Between  350°  and 
500°,  the  specific  conductance  increases  approximately  60  per  cent,  which 
corresponds  roughly  to  an  increase  of  %  per  cent  per  degree.  The  fluidity 
varies  somewhat  more  than  the  conductance  over  the  same  temperature 

interval,  so  that,  as  the  temperature  rises,  the  value  of  the  ratio  H  de- 

r 

creases.    It  is  interesting  to  note  that  the  value  of  -^  is  near  unity,  which 

r 

differs  not  greatly  from  the  value  of  -^  for  electrolytic  solutions,  par- 

r 

ticularly  in  the  case  of  water.  This  may  be  taken  to  indicate  that  the 
fused  salts  are  highly  ionized. 

For  different  fused  salts,  the  conductance  is  of  the  same  order  of 
magnitude,  corresponding  to  the  fact  that  they  have  approximately  the 
same  fluidity.  In  Table  CXXXVI  are  given  values  of  the  specific  con- 
ductance \i,  the  equivalent  conductance  A,  and  the  fluidity  F,  together 

with  the  ratio  -^  for  different  salts.     It  will  be  observed  that  the  ratio 

r 

TABLE   CXXXVI. 
VALUES  OF  A  AND  F  FOR  DIFFERENT  FUSED  SALTS. 

\i  A  F  A/F 

350°C.            NaN03   .: 1.173  52.88  42.6  1.24 

KN03   0.6728  36.54  38.0  0.96 

"                 AgN03 1.245  55.43  45.5  1.22 

310°C.            LiN03 1.126  44.21  27.2  1.62 

250°C.  AgC103    1.4743  27.72 

-=i  is  of  the  same  order  for  the  different  salts.  In  the  case  of  the  nitrates 
r 

the  ratio  is  smallest  for  potassium  nitrate  and  greatest  for  lithium  nitrate. 

The  order  of  the  ratio  •=•  corresponds  to  the  order  of  the  atomic  volumes, 
r 


PURE  SUBSTANCES,  FUSED  SALTS,  SOLID  ELECTROLYTES      355 

Jaeger  and  Kapma6a  have  measured  the  specific  conductance  and  the 
densities  of  potassium  nitrate,  sodium  nitrate,  lithium  nitrate,  rubidium 
nitrate,  caesium  nitrate,  potassium  fluoride,  potassium  chloride,  potas- 
sium bromide,  potassium  iodide,  sodium  molybdate,  and  sodium  tung- 
state  over  considerable  temperature  ranges.  At  a  given  temperature,  the 
equivalent  conductance  of  the  different  salts  is  of  the  same  order  of 
magnitude.  For  the  nitrates  the  conductance  increases  in  order  from 
caesium  to  lithium.  For  the  potassium  halide  salts,  the  conductance  is 
smallest  for  the  fluoride  and  greatest  for  the  chloride,  while  that  of  the 
iodide  and  bromide  is  intermediate  between  them. 

The  conductance  increases  very  nearly,  although  not  quite,  as  a 
linear  function  of  the  temperature.  The  temperature  coefficients  vary 
appreciably,  being  greatest  for  potassium  fluoride  and  smallest  for 
caesium  nitrate. 

The  conductance  of  mixtures  of  fused  salts  is  very  nearly  a  linear 
function  of  the  composition.  In  the  following  table  are  given  values  of 
the  conductance  of  mixtures  of  sodium  and  potassium  nitrates  at  450°, 

together  with  the  values  of  F  and  of  -^.7a    It  will  be  observed  that  as  the 

r 

concentration  changes  the  conductance  varies  continuously  between  that 
of  the  two  components. 

TABLE  CXXXVII. 

CONDUCTANCE  OF  MIXTURES  OF  SODIUM  AND  POTASSIUM  NITRATES  AT  450°. 

100  molar  %  KN03 
0.973 
55.03 
60.2 
0.915 

The  fact  that  in  the  mixtures  of  fused  salts  the  conductance  is  approxi- 
mately a  linear  function  of  the  composition  shows  that  no  considerable 
reaction  takes  place  on  mixing.  This  indicates  a  high  degree  of  ioniza- 
tion  of  the  fused  electrolyte. 

In  Table  CXXXVIII  are  given  values  of  the  conductance  of  mixtures 
of  silver  iodide  and  silver  bromide  at  550°. 7  Here,  again,  the  conduc- 

TABLE   CXXXVIII. 
CONDUCTANCES  OF  MIXTURES  OF  SILVER  IODIDE  AND  SILVER  BROMIDE. 

%AgBr  0         5       10       20       30       40       60       70       80       90      100 
pi....  2.36    2.40    2.39    2.41     2.43    2.50    2.64    2.67    2.68    2.84    3.00 

88  Jaeger  and  Kapma,  Ztschr.  f.  Anorg.  Chem.  113,  27   (1920). 

T«  Goodwin  and  Mailey,  loc.  cit. 

TTubandt  and  Lorenz,  Ztschr.  f.  phya,  Chem.  87,  543  (1914). 


0 

20 

50 

80 

n  .. 

1.562 

1.389 

1.205 

1.059 

A  .. 

73.15 

67.84 

62.56 

57.96 

F   .. 

65.7 

66.3 

63.3 

A/F   .. 

1.12 

0.945 

0.915 

356       PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

tance  varies  continuously  between  that  of  the  two  components.  It  is 
true  that  a  few  irregularities  occur,  but  these  are  small  and  probably  lie 
within  the  limits  of  experimental  error.  The  fused  salts  are  characterized 
by  the  great  similarity  in  their  behavior.  As  has  already  been  pointed 
out,  the  order  of  magnitude  of  the  conductance  is  the  same  for  all  typical 
fused  salts. 

In  the  following  table  are  given  values  of  the  conductance  of  thallium 
and  silver  salts  at  600°  .8 

TABLE  CXXXIX. 
CONDUCTANCE  OF  THALLOTJS  AND  SILVER  SALTS  AT  600°. 

Til 0.840  Agl    2.43 

TIBr 1.127  AgBr 3.08 

T1C1 1.700  AgCl  4.16 

In  both  cases,  the  conductance  of  the  salt  increases  in  the  order:  iodide, 
bromide,  chloride.  The  conductance  of  the  silver  salts  is  markedly 
greater  than  that  of  the  thallium  salts. 

A  great  many  data  are  available  relating  to  the  conductance  of  fused 
salts,9  but,  in  view  of  the  similarity  in  the  behavior  of  the  different  fused 
salts,  it  is  unnecessary  to  give  here  in  detail  the  various  observations 
which  have  been  recorded.  Thus  far,  the  subject  has  been  studied  chiefly 
from  an  empirical  point  of  view  and  we  possess  but  little  knowledge  of 
the  molecular  condition  of  these  substances. 

The  form  of  the  conductance  curve  of  mixtures  of  sodium  and  potas- 
sium nitrate  and  of  silver  chloride,  iodide  and  bromide  indicates 
that  in  these  mixtures  complex  ions  are  not  formed.  In  some  other  in- 
stances, however,  there  is  a  probability  that  complex  ions  may  exist.10 
This  is  the  case,  for  example,  with  mixtures  of  potassium  chloride  and 
lead  chloride.  Lorenz  has  carried  out  transference  measurements  which 
indicate  that  a  complex  of  the  type  K2PbCl4  is  probably  formed  in  the 
mixture. 

3.  Conductance  of  Glasses.  For  want  of  a  suitable  reference  sub- 
stance, transference  measurements  with  the  fused  salts  have  not  been 
carried  out,  and  as  a  consequence  we  lack  any  knowledge  as  to  the  pro- 
portion of  the  current  carried  by  the  two  ions  in  these  electrolytes.  In 
a  few  instances,  however,  particular  systems  have  been  investigated  in 
which  the  current  is  carried  entirely  by  either  the  positive  or  the  nega- 

•  Tubandt  and  Lorenz,  loc.  cit. 

9  Lorenz.  "Electrolyse  geschmolzener  Salze,  Monographien  u.  Angew.  Electrocb,"  20 
(1905). 

»  Lorenz,  Ztschr.  /.  phya.  Chew.  70,  230   (1910). 


PURE  SUBSTANCES,  FUSED  SALTS,  SOLID  ELECTROLYTES      357 

tive  ion.  Among  those  substances  which  may  be  classed  strictly  as  fused 
salts  are  the  glasses.  A  glass  is  to  be  considered  as  a  supercooled  liquid 
which  is  mechanically  rigid.  Usually,  glasses  consist  of  mixtures  of 
silicates  of  the  alkali  metals  and  the  metals  of  the  alkaline  earths.  What 
the  nature  of  the  compounds  is  in  these  systems  is  not  known.  Doubt- 
less, the  silica  is  present  in  the  electronegative  constituent.  It  is  well 
known  that  ordinary  glasses  are  excellent  conductors  of  the  current  at 
high  temperatures,  the  conductance  increasing  with  the  temperature.  In 
general,  the  conductance-temperature  curve  is  exponential  in  form. 

In  the  following  table  are  given  values  of  the  resistance  of  ordinary 
soda-lime  glass  at  different  temperatures.11 

TABLE  CXL. 
RESISTANCE  OF  ORDINARY  SODA  GLASS  AT  DIFFERENT  TEMPERATURES. 

Temperature  C....  325  355  404  469  484  500  540 
Resistance 9200  1900  687  172  133  89  2.4 

It  will  be  observed  that,  even  at  temperatures  as  low  as  325°,  glass  con- 
ducts the  current  with  measurable  facility,  while  in  the  neighborhood  of 
its  softening  point,  540°,  it  conducts  extremely  well.  To  what  the  great 
increase  in  the  conductance  of  glass  is  due  is  uncertain.  We  shall  see 
below  that  the  ionization  of  a  glass  varies  only  little  as  a  function  of  the 
temperature  and  consequently  the  increased  conductance  must  be  due 
to  the  increased  speed  of  the  ions.  The  nature  of  the  frictional  resist- 
ance which  the  ions  meet  in  their  motion  through  a  glass  is,  however, 
uncertain.  At  temperatures  below  400°,  glasses  of  this  type  appear  to 
be  entirely  rigid  and  consequently  the  increased  conductance  is  not 
simply  related  to  the  mechanical  rigidity  of  the  glass. 

The  conduction  process  in  the  case  of  the  glasses  is  electrolytic  in 
character.1111  If  a  current  is  passed  through  a  glass  tube  from  a  sodium 
nitrate  anode  to  a  mercury  cathode,  metal  is  transferred  from  the  sodium 
nitrate  to  the  mercury  through  the  glass  in  accordance  with  Faraday's 
law  and  no  change  whatever  takes  place  in  the  glass  itself.  This  indi- 
cates that  the  conduction  process  in  such  glasses  is  due  to  the  motion 
of  the  sodium  ion  and  is  not  due  to  the  motion  of  an  electronegative  ion. 
This  type  of  conduction  is  characteristic  of  many  rigid  electrolytic  con- 
ductors. Since  positively  charged  carriers  are  present  within  the  glass, 
it  is  obvious  that  negative  carriers  must  likewise  be  present.  The  nega- 
tive carriers,  however,  must  form  a  substantially  rigid  system,  since  they 
take  no  part  in  the  conduction  process.  It  is  also  evident  that,  in  the 

"Darby,  Thesis,  Clark  University  (1917). 

"»  LeBlanc  and  Kerschbaum,  Ztschr.  f.  phys.  Chem.  12,  468   (1910). 


358       PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

case  of  the  glasses,  the  ions  consist  of  the  atoms  themselves,  since,  on 
passing  a  current  through  soda-lime  glass,  the  only  material  transferred 
is  sodium.  This  and  similar  cases  are  the  only  ones  in  which  it  has 
been  definitely  demonstrated  that  an  electrolytic  ion  consists  of  a  charged 
atom  alone. 

In  the  case  of  glasses,  it  is  possible  to  substitute  the  sodium  ion  by 
another  positive  ion.llb  Such  a  substitution  is,  in  effect,  a  determina- 
tion of  the  speed  of  the  ions  by  the  moving  boundary  method.  Substitu- 
tion may  be  quite  generally  effected  but,  in  the  case  of  most  positive  ions, 
the  glass  disintegrates  as  the  process  proceeds.  In  the  case  of  silver, 
however,  a  substitution  may  be  carried  out  to  a  considerable  depth.  If 
sodium  is  substituted  by  silver,  the  weight  of  the  glass  is  increased  in 
proportion  to  the  difference  in  the  atomic  weight  of  silver  over  that  of 
sodium.  In  the  following  table  are  given  values  of  the  gain  in  weight 
of  a  sample  of  soda  glass,  together  with  the  values  calculated  from  the 
amount  of  electricity  passed  as  determined  in  a  coulometer.110  The  tem- 
perature is  given  in  the  first  column. 

TABLE   CXLI. 

OBSERVED  AND  CALCULATED  GAIN  IN  WEIGHT  OF  SODA  GLASS  ON 
SUBSTITUTION  BY  SILVER. 

Gain  in  Weight  Gain  in  Weight 
Temperature                  Calculated  Observed 

350°  0.0339  g.  0.0347  g. 

350°  0.0396  0.0416 

343°  0.0732  0.0762 

343°  0.0209  0.0209 

By  measuring  the  penetration  of  the  silver  boundary  into  the  glass 
under  a  given  potential  gradient,  it  is  possible  to  determine  the  volume 
of  the  glass  which  has  been  affected,  and,  knowing  the  composition  of 
the  glass,  it  is  possible  to  determine  the  fraction  of  sodium  in  the  glass 
replaced  by  silver.  This  has  been  done  in  the  case  of  soda  glass  with 
the  following  results.110 

TABLE   CXLII. 
RELATIVE  AMOUNTS  OF  SODIUM  REPLACED  BY  SILVER  IN  SODA  GLASS. 

|  *  1% 

278°  76.5 

295°  76.8 

323°  77.05 

343°  82.3 

ub  Heydweiller  and  Kopfermann,  Ann,  d.  Phya.  32,  729  (1910). 
»«  Darby,  loo.  cit. 


PURE  SUBSTANCES,  FUSED  SALTS,  SOLID  ELECTROLYTES      359 

While  these  values  are  not  very  precise,  nevertheless,  they  clearly  indi- 
cate that  about  three- fourths  of  the  sodium  present  in  these  glasses  may 
be  electrolyzed  out  and  replaced  by  another  metal.  The  effective  ioniza- 
tion  of  the  sodium  in  soda  glass,  therefore,  is  of  the  order  of  magnitude 
of  75  per  cent.  This  is  apparently  the  only  direct  determination  which 
has  thus  far  been  made  of  the  relative  amount  of  a  substance  actually 
concerned  in  the  conduction  process  in  an  electrolyte.  If  so  large  a 
proportion  of  the  sodium  in  soda  glass  is  actually  concerned  in  the  con- 
duction process,  it  is  reasonable  to  assume  that  the  fused  salts  are  very 
nearly  completely  ionized.  It  is  interesting  to  note  that,  as  the  tempera- 
ture rises,  the  ionization  of  sodium  in  glass  increases  slightly. 

Since  the  penetration  of  the  silver  is  determined  solely  by  the  rate 
of  motion  of  the  ions  and  since  the  conduction  is  due  entirely  to  the  posi- 
tive ion,  it  follows  that  the  depth  of  penetration  should  be  proportional 
to  the  specific  conductance  or  inversely  proportional  to  the  specific  resist- 
ance of  the  glass.  This  condition  is  in  general  fulfilled. 

From  the  preceding  data  it  is  possible  to  calculate  the  speed  of  the 
sodium  ion  in  glasses;  that  is,  the  speed  with  which  this  ion  moves  under 
a  potential  gradient  of  one  volt  per  centimeter.  In  the  following  table 
are  given  values  of  the  absolute  speed  of  the  sodium  ion  at  different 
temperatures. 

TABLE    CXLIII. 

ABSOLUTE  SPEED  OF  THE  SODIUM  ION  IN  SODA  GLASS  AT  DIFFERENT 

TEMPERATURES. 

278°  4.52  X  10-8 

295°  1.46  X  10-r 

323°  3.26  X  10'7 

343°  5.9  X  10-6 

It  will  be  observed  that,  as  might  be  expected,  the  absolute  speed  of  the 
sodium  ion  is  relatively  very  low.  On  the  other  hand,  corresponding  to 
the  greatly  increased  conductance  of  glass  with  increasing  temperature, 
the  speed  of  the  sodium  ion  increases  largely  with  temperature. 

4.  Solid  Electrolytes.  Solid  substances,  both  crystalline  and  amor- 
phous, conduct  the  electric  current  with  more  or  less  facility.  In  the 
case  of  the  insulators,  where  the  conductance  is  of  an  extremely  low 
order,  it  is  not  unlikely  that  conductance  is  due  to  the  presence  of  traces 
of  impurities.  The  only  substance  for  which  this  has  actually  been 
shown  is  crystalline  quartz,  in  which  the  conductance  is  due  to  the  pres- 
ence of  traces  of  sodium  as  impurity.12  Here  the  current  is  carried  by 

»  Warburg  and  Tegetmeier,  Ann.  d.  Phys.  35,  455  (1888). 


360       PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 


the  sodium  ion  which  alone  is  capable  of  motion  in  these  crystals.  The 
process  of  conduction  appears  to  be  entirely  similar  to  that  in  glasses. 
The  typical  salts,  below  their  melting  point,  conduct  the  current,  in 
some  cases,  with  extreme  facility.  As  a  rule,  the  conductance  increases 
with  increasing  temperature  according  to  an  exponential  curve.  The 
specific  conductance  may  be  expressed  fairly  well  as  a  function  of  tem- 
perature by  means  of  the  equation: 


(132) 


log  [i  =  a  +  bt, 


where  a  and  b  are  constants.  In  the  following  table  are  given  values  of 
the  specific  conductance  of  a  few  salts  at  temperatures  through  their 
melting  points.18 

TABLE    CXLIV. 

CONDUCTANCE  OF  SALTS  THROUGH  THE  MELTING  POINT. 


T1C1 


AgCl 


250° 

0.00005 

300 

0.00024 

350 

0.0009 

400 

0.0037 

427  (M.P.) 

(  0.0067 
(1.082 

450 

1.17 

500 

1.332 

600 

1.700 

AgBr 


200° 

240 

280 

350 

400 

419 

422 

425 

500 

600 


0.00052 

0.0023 

0.0091 

0.08 

0.38 

0.51 

M.P. 

2.76 

2.92 

3.08 


t 

250° 

300 

350 

400 

450 

455 

456 

500 

600 


t 

125° 
140 

144.6 

150 
250 
350 
450 
550 
552 
554 
600 
650 


Agl 


0.00030 

0.0015 

0.0065 

0.026 

0.11 

M.P. 
3.76 
3.91 
4.16 


0.00011 

0.00026 
(0.00034 
(1.31 

1.33 

1.78 

2.14 

2.41 

2.64 

M.P. 

2.36 

2.43 

2.47 


11  Tubandt  and  Lorenz,  Ztschr.  f.  phys.  Chem.  87,  513   (1914). 


PURE  SUBSTANCES,  FUSED  SALTS,  SOLID  ELECTROLYTES      361 


Temperature. 

FIG.  62.    Specific  Conductance  of  Silver  Halides  at  Various  Temperatures  Through 

Their  Melting  Points. 

The  relation  between  the  conductance  and  the  temperature  is  shown 
graphically  in  Figure  62.  In  general,  the  conductance  of  the  solid  salt 
increases  with  temperature  according  to  Equation  132  up  to  the  melting 


362        PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

point,  where  a  discontinuity  occurs,  a  large  increase  taking  place  on 
fusion.  Silver  iodide,  however,  forms  an  exception  to  this  rule.  This 
substance  exhibits  a  transition  point  at  144.6°.  Below  this  temperature 
the  conductance  of  silver  iodide  increases  with  temperature  in  a  manner 
similar  to  that  of  silver  chloride  and  bromide.  At  the  transition  point, 
the  specific  conductance  increases  from  a  value  of  3.4  x  10~4  to  1.31. 
Beyond  the  transition  point,  the  conductance  of  silver  iodide  increases 
slowly  with  the  temperature,  the  temperature  coefficient  being  not  greatly 
different  from  that  of  fused  salts,  as  may  be  seen  from  the  figure.  It 
will  be  observed,  furthermore,  that  at  the  melting  point  the  conductance 
of  solid  silver  iodide  is  markedly  higher  than  that  of  the  fused  salt,  the 
conductance  on  melting  decreasing  from  2.64  to  2.36.  Even  at  the  tran- 
sition point,  at  a  temperature  as  low  as  144.6,  the  specific  conductance 
of  solid  silver  iodide  is  of  the  order  of  magnitude  of  that  of  fused  salts. 
This  is  a  remarkable  phenomenon  and  shows  that  the  power  of  con- 
ducting the  current  with  facility  is  by  no  means  restricted  to  the  liquid 
state.  Thus  far,  however,  silver  iodide  is  the  only  solid  salt  whose  con- 
ductance in  the  solid  state  has  been  found  to  be  comparable  with  that 
in  the  liquid  state  far  below  its  melting  point. 

The  conduction  process  in  solid  salts  of  this  type  is  purely  electrolytic, 
as  follows  from  the  fact  that  Faraday's  Law  holds  true  within  the  limits 
of  experimental  error.  In  the  following  table  are  given  the  observed 
amounts  of  silver  precipitated  on  electrolysis,  together  with  the  amounts 
of  silver  precipitated  in  a  silver  coulometer  carrying  the  same  current.14 

TABLE   CXLV. 
TEST  OF  FARADAY'S  LAW  IN  SOLID  ELECTROLYTES. 

Ag  Ag 

Dissolved     Precipitated 
Electrolyte  Temperature   at  Anode    in  Coulometer      %  Dif. 

Silver  Iodide 540°  0.7212  0.7139  + 1.20 

"          "        540  0.5642  0.5623  +0.34 

150  0.7841  0.7804  +0.48 

150  0.7767  0.7706  +0.80 

Silver  Bromide 400  0.5883  0.5842  +  0.70 

Silver  Chloride   430  0.3779  0.3751  +0.75 

Considering  the  small  amount  of  silver  precipitated  or  dissolved  and 
the  difficulty  of  carrying  out  the  experiments,  the  agreement  between 
the  observed  and  the  calculated  values  of  the  amount  of  silver  dissolved 

"Tubandt  and  Lorenz,  loo.  cit. 


PURE  SUBSTANCES,  FUSED  SALTS,  SOLID  ELECTROLYTES      363 

at  the  anode  is  remarkably  good.  The  applicability  of  Faraday's  Law 
has  been  further  verified  by  Tubandt  and  Eggert.15  There  can  be  little 
question  but  that,  in  the  case  of  these  salts,  Faraday's  Law  holds  true. 

By  employing  solid  silver  iodide  above  its  transition  point  in  contact 
with  a  silver  cathode,  Tubandt 16  has  found  it  possible  to  test  Faraday's 
law  in  the  case  of  other  electrolytes  than  the  silver  salts  and,  further- 
more, has  been  able  to  carry  out  transference  measurements  in  order  to 
determine  to  what  extent  the  conductance  in  solid  electrolytes  is  due  to 
the  positive  and  to  what  extent  it  is  due  to  the  negative  carrier.  It  has 
been  shown  that  for  silver  iodide,  silver  bromide,  silver  chloride,  silver 
sulphide,  above  its  transition  point,  and  copper  sulphide  (Cu2S),  Fara- 
day's Law  holds  and  that  in  these  salts  the  current  is  carried  entirely  by 
the  positive  ion.  These  results  are  very  significant  in  that  they  show 
that  one  set  of  ions  in  these  solids  forms  a  fixed  framework  through  which 
the  other  ions  move  with  considerable  facility.  In  the  above  salts,  the 
negative  ions  form  the  framework  through  which  the  positive  ions  move. 
In  lead  chloride,  however,  the  current  is  carried  by  the  negative  ion; 
the  positive  ions  form  the  framework  through  which  the  negative  ions 
move.  These  facts  have  an  important  bearing  on  the  theory  of  the 
structure  of  solid  salts. 

Silver  sulphide  has  a  transition  point  at  179°.  Above  the  transition 
temperature,  as  was  shown  by  actual  electrolysis  of  the  salt,  Faraday's 
Law  holds  and  the  current  is  carried  entirely  by  the  positive  ions.  Below 
the  transition  temperature,  the  (3  form  of  silver  sulphide  appears  to  con- 
duct in  part  metallically.  In  the  (3  form  of  silver  sulphide,  Faraday's 
Law  does  not  hold,  only  about  80  per  cent  of  the  current  being  carried 
by  the  silver  ion.  The  negative  ion  in  this  case  is  apparently  not  in- 
volved in  the  conduction  process,  the  remainder  of  the  current  being 
carried  by  a  metallic  process  of  conduction.  Apparently,  therefore,  solid 
electrolytes  exist  in  which  the  current  is  carried  partly  metallically  and 
partly  electrolytically.  As  we  shall  see  in  a  subsequent  chapter,  solu- 
tions of  the  alkali  metals  in  liquid  ammonia  likewise  conduct  the  cur- 
rent by  a  mixed  process. 

The  conductance  of  a  heterogeneous  mixture  of  two  solid  electrolytes 
is  approximately  a  linear  function  of  the  composition  of  the  mixture. 
When  two  solid  electrolytes  form  mixed  crystals,  however,  the  conduc- 
tance of  the  homogeneous  mixture  is  often  much  greater  than  that  of 
the  pure  constituents.  In  the  following  table  are  given  values  of  the 

"Tubandt  and  Eggert,  Ztschr.  J.  anorg.  Cliem.  110,  196  (1920) 
"Tubandt,  Ztschr.  f.  Electroch.  26,  358   (1920). 


364        PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

specific  conductance  \i  x  106  of  mixtures  of  sodium  chloride  and  potas- 
sium chloride  at  570°. 17 

TABLE  CXLVI. 
CONDUCTANCE  OF  MIXTURES  OF  SODIUM  AND  POTASSIUM  CHLORIDE  AT  570°. 

%NaCl  0         10        20         30         40         50        60        70         80         90       100 

pXlO6    0.87      8.0      16.5      22.0      24.0      24.0      30.0      34.5      40.0      28.0      4.5 

The  conductance  value  of  0.87  for  pure  potassium  chloride  at  570° 
has  been  calculated  from  the  conductance  values  at  somewhat  higher 
temperatures  by  means  of  Equation  132.  It  will  be  observed  that  the 
conductance  curve  exhibits  a  maximum  in  the  neighborhood  of  80  per 
cent  of  sodium  chloride,  at  which  point  the  conductance  of  the  mixture 
is  nearly  ten  times  that  of  pure  sodium  chloride  and  forty  times  that  of 
pure  potassium  chloride.  Apparently,  the  maximum  lies  toward  the 
side  of  that  component  which  possesses  the  higher  conductance.  Other 
systems  of  mixed  crystals  have  yielded  similar  results.  Apparently, 
therefore,  it  is  a  general  rule  that  the-  conductance  of  mixed  crystals  is 
much  greater  than  that  of  the  pure  components. 

In  the  case  of  mixtures  of  silver  iodide  with  silver  bromide  and  with 
silver  chloride,  the  conductance-temperature  curve  of  the  resulting  mix- 
ture exhibits  discontinuities  as  a  result  of  the  peculiar  nature  of  silver 
iodide.18  Up  to  80  per  cent  of  silver  bromide,  a  homogeneous  phase  re- 
sults initially,  whose  conductance  curve  corresponds  with  that  of  silver 
iodide  above  the  transition  temperature  of  146.5°.  Apparently,  then,  in 
these  mixed  crystals,  the  silver  bromide  is  present  in  a  condition  similar 
to  that  of  silver  iodide  above  its  transition  point.  The  details  of  the 
conductance  curves  of  these  mixtures  need  not  be  discussed  further  here. 
It  may  be  noted,  however,  that  a  study  of  the  conductance  of  various 
solid  systems  is  capable  of  throwing  light  on  the  phase  relations  in  these 
systems. 

It  will  be  evident  from  the  foregoing  discussion  that  solid  electrolytes 
exhibit  a  marked  variety  of  phenomena  which  have  an  important  bearing 
on  our  conceptions  of  the  nature  of  the  conduction  process,  as  well  as 
upon  that  of  the  structure  of  solid  salts.  The  available  data  are  as  yet 
extremely  meager,  but  it  may  be  expected  that,  as  this  field  is  further 
developed,  results  of  great  value  will  be  obtained. 

5.  Lithium  Hydride.  The  conductance  of  lithium  hydride,  both  in 
the  solid  and  in  the  liquid  condition,  has  been  investigated  by  Moers.19 

17  Benrath  and  Wainoff,  Ztschr.  f.  physt  Chem.  11,  257    (1911). 

u  Tubandt  and  Lorenz,  loc.  cit. 

19Moers,  Ztschr.  f.  anorg.  Chem.  113,  179   (1920). 


PURE  SUBSTANCES,  FUSED  SALTS,  SOLID  ELECTROLYTES      365 

In  the  following  table  are  given  values  of  the  specific  conductance  of 
lithium  hydride  at  different  temperatures. 

TABLE    CXLVII. 

SPECIFIC  CONDUCTANCE  OF  LITHIUM  HYDRIDE  AT  DIFFERENT 
TEMPERATURES. 

t  p  t  |i 

443°  2.124  X10-5  661.5°  2.018  X  1Q-2 

507  2.113  X10-4  685  3.206  X  10~2 

556  8.447  X  10"4  725  7.59S  X  10"2 

570  1.491  X  10-3  734  1.125  X  10'1 

597  3.225X10-3  754  1.01 

638  1.139  X  10-2 

The  values  of  the  specific  conductance  may  be  represented  by  means 
of  a  sum  of  terms  in  ascending  powers  of  the  temperature.  It  is  interest- 
ing to  note  that  the  same  equation  applies  both  above  and  below  the 
melting  point  of  lithium  hydride,  which  is  680°.  Apparently,  therefore, 
there  is  no  discontinuity  in  the  conductance  of  this  hydride  at  its  melt- 
ting  point.  This  behavior  is  exceptional. 

This  salt  exhibits  polarization  when  a  direct  current  is  passed  through 
it,  and  it  has  been  shown  that,  on  the  passage  of  the  current,  lithium  is 
deposited  at  the  cathode  and  hydrogen  evolved  at  the  anode.  The  cur- 
rent is  therefore  conducted  by  either  one  or  both  of  the  ions  Li+  and  H~. 
This  salt,  therefore,  presents  a  very  interesting  case,  not  only  in  that  the 
conductance  of  the  solid  is  the  same  as  that  of  the  liquid  at  its  melting 
point,  but,  also,  in  that  hydrogen  appears  here  as  a  negative  ion.  This 
is  the  only  case  so  far. observed  in  which  hydrogen  has  been  shown  to 
function  in  this  manner. 

The  behavior  of  hydrogen  in  lithium  hydride  is  thus  very  similar  to 
that  of  certain  metallic  elements  in  their  compounds  with  the  alkali 
metals  in  liquid  ammonia,  referred  to  in  a  preceding  chapter.  We  saw 
there  that,  for  example,  in  a  solution  containing  lead  and  sodium,  lead 
is  dissolved  at  the  cathode  and  precipitated  at  the  anode.  In  the  pres- 
ence of  very  electropositive  elements,  less  electropositive  elements  tend  to 
take  up  negative  electrons  and  function  as  anions.  This  dual  function 
of  many  elements,  which  ordinarily  act  as  cations,  is  very  significant 
from  the  standpoint  of  the  constitution  of  many  compounds  in  which 
these  elements  are  involved. 


Chapter  XIV. 

Systems  Intermediate  Between  Metallic  and  Electrolytic 

Conductors. 

1.  Distinctive  Properties  of  Metallic  and  Electrolytic  Conductors. 
Substances  which  possess  the  power  of  conducting  the  electric  current 
are,  in  the  main,  sharply  divided  into  two  classes;  namely,  metallic 
and  electrolytic  conductors.  The  members  of  each  of  these  two  classes 
of  conducting  substances  have  many  properties  in  common  with  one 
another,  which  properties  serve  to  distinguish  the  members  of  one  class 
from  those  of  the  other.  It  is  in  their  optical  and  electrical  properties 
that  the  members  of  the  two  classes  exhibit  the  greatest  contrast.  While 
electrolytic  systems,  in  general,  are  transparent,  metallic  systems  are 
non-transparent  and  exhibit  metallic  reflection.  Electrolytic  systems 
conduct  the  current  with  the  accompaniment  of  material  effects,  while 
metallic  systems  conduct  the  current  without  attendant  material  effects 
of  any  kind.  Nevertheless,  the  view  has  been  gradually  gaining  ground 
that  the  conduction  process  in  the  two  systems  is  similar  in  that  conduc- 
tion is  effected  by  the  motion  of  charged  particles.  While  we  possess  a 
more  or  less  comprehensive  theory  of  the  mechanism  whereby  the  transfer 
of  the  charge  is  affected  in  electrolytic  systems.,  a  similar  theory  does 
not  exist  for  metallic  systems.  Such  knowledge  as  we  do  possess  regard- 
ing the  existence  of  charged  particles  in  metals  is  founded  chiefly  on 
observations  on  the  properties  of  metals  other  than  those  relating  imme- 
diately to  the  conduction  process.  There  exists  little  direct  evidence 
showing  that  the  passage  of  the  current  through  the  metals  is  effected 
by  the  motion  of  charged  particles. 

The  great  difficulty  in  the  way  of  a  direct  attack  on  the  problem  of 
metallic  conduction  lies  in  the  absence  of  material  effects  accompanying 
the  passage  of  the  current.  In  addition,  there  has  been  a  complete  lack 
of  systems  exhibiting  properties  intermediate  between  those  of  metallic 
and  electrolytic  conductors.  Conducting  systems  fall  sharply  into 
one  of  two  classes;  namely,  metallic  and  electrolytic  conductors.  In 
recent  years,  however,  a  class  of  solutions  has  been  subjected  to  investi- 
gation which  appears  to  bridge  the  gap  between  metallic  and  electrolytic 
conductors;  in  other  words,  which  exhibits  properties,  on  the  one  hand,  in 

366 


SYSTEMS  INTERMEDIATE  367 

common  with  those  of  metallic  systems  and,  on  the  other  hand,  with 
those  of  electrolytic  systems.1  These  are  solutions  of  the  alkali  metals 
and  the  metals  of  the  alkaline  earth  in  liquid  ammonia  and  organic 
derivatives  of  ammonia.  In  order  to  make  clear  the  bearing  of  these 
solutions  on  the  problem  of  metallic  conduction,  it  will  be  necessary  to 
discuss  in  some  detail  the  properties  of  these  solutions  of  the  metals  in 
liquid  ammonia. 

2.  Nature  of  the  Solutions  of  the  Metals  in  Ammonia.  The  alkali 
metals  are  extremely  soluble  in  liquid  ammonia,  yielding  solutions  whose 
external  appearance  depends  upon  their  concentration.  Dilute  solutions 
of  the  alkali  metals,  as  well  as  of  metals  of  the  alkaline  earths,  exhibit  a 
fine  blue  color,  whose  absorption  for  all  wave  lengths  is  relatively 
great.1*  At  higher  concentrations,  the  solutions  possess  a  marked  re- 
flecting power  for  all  wave  lengths.  Very  concentrated  solutions  exhibit 
distinct  metallic  reflection  of  a  color  intermediate  between  that  of  copper 
and  gold.  Among  the  earlier  investigators  of  these  solutions  there  was 
much  discussion  as  to  whether  the  metal  exists  in  solution  as  such  or  as 
a  compound  with  the  solvent.  Cady 2  showed  that  these  solutions  are 
excellent  conductors  of  the  electric  current  and  that  in  concentrated 
solutions  the  passage  of  the  current  is  characterized  by  the  absence  of 
polarization  effects  at  the  electrodes.  Finally,  it  has  been  shown  that, 
in  the  case  of  the  alkali  metals,  stable  compounds  between  the  metals 
and  the  solvent  cannot  be  separated  from  these  solutions.8  While  com- 
pounds between  the  metal  and  the  solvent  may  exist  in  solution,  such 
compounds,  if  they  exist,  possess  little  stability  as  follows  from  the  low 
value  of  the  energy  changes  accompanying  the  process  of  solution.  In 
the  case  of  the  metals  of  the  alkaline  earths,  however,  it  has  been  shown 
that  compounds  may  be  separated  from  solution,  in  which  the  metal  is 
combined  with  ammonia.  Kraus  has  prepared  the  compound  Ca(NH3)6 
and  recently  Biltz 4  has  prepared  the  compounds  Ba(NH3)6  and 
Sr(NH3)6.  These  compounds  possess  a  metallic  appearance,  resembling 
that  of  the  concentrated  solutions  of  the  metals  in  ammonia. 

Kraus  has  determined  the  vapor  pressure  of  solutions  of  sodium  in 
liquid  ammonia,  from  which  he  calculated  the  molecular  weight  of  the 
metal  in  these  solutions.  Since  the  molecular  weight  can  be  determined 
only  in  dilute  solutions,  where  the  properties  of  the  system  are  approach- 
ing those  of  an  ideal  system,  it  follows  that  molecular  weight  determina- 

1  Kraus,  J.  Am.  Chem.  Soc.  £9,  1557  (1907)  ;  ibid.,  SO,  653,  1157  and  1323  (1908)  ; 
iMd.,  S6,  864  (1914)  ;  ibid.,  43,  749  (1921). 

la  Gibson  and  Argo,  J.  Am.  Chem.  Soc.  40,  1327   (1918). 
8  Cady,  J.  Phys.  Chem.  1,  707  (1897). 
•Kraus,  J.  Am.  Chem.  Soc.  SO,  653   (1908). 
«3iltz,  Zfschr.  f.  Electroch.  %6,  374   (1920), 


368        PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

tions  are  always  more  or  less  in  doubt.  However,  if  the  molecular  weights 
are  determined  at  a  series  of  concentrations,  it  is  possible  to  draw  an 
inference  as  to  the  limit  approached,  as  the  concentration  of  the  solution 
decreases,  from  the  manner  in  which  the  apparent  molecular  weight 
varies  as  a  function  of  the  concentration.  In  the  following  table  are 
given  values  of  the  apparent  molecular  weight  of  sodium  dissolved  in 
liquid  ammonia  at  different  concentrations,  and  in  Figure  63  are  shown 
these  values  plotted  as  ordinates  against  the  logarithms  of  the  concen- 
trations as  abscissas. 

TABLE   CXLVIII. 

APPARENT  MOLECULAR  WEIGHT  OF  SODIUM  IN  AMMONIA  AT 
DIFFERENT  CONCENTRATIONS. 

C  Apparent  Mol.  Wt.  C  Apparent  Mol.  Wt. 

2.903  32.23  0.3665  25.31 

1.841  30.70  0.3587  25.27 

1.220  29.06  0.2669  23.53 

0.9910  28.80  0.2516  23.43 

0.9038  28.46  0.2261  23.41 

0.5614  26.39  0.1565  21.62 

0.5558  26.47  0.1519  21.58 

0.4104  25.36 

It  will  be  seen  that,  as  the  concentration  decreases,  the  calculated  value 
of  the  molecular  weight  decreases  very  nearly  as  a  linear  function  of 
the  logarithm  of  the  concentration  over  the  ranges  of  concentration 
investigated.  It  is  not  possible  to  state  what  value  the  molecular  weight 
approaches  as  a  limit,  but  it  is  evident  that  the  limit  approached  has  a 
value  less  than  23,  the  atomic  weight  of  sodium.  It  appears,  therefore, 
that  sodium  dissolved  in  liquid  ammonia  exists  in  an  atomic  condition 
and  it  is  probable  that  the  limit,  which  the  molecular  weight  approaches, 
has  a  value  less  than  the  atomic  weight  of  sodium.  This  indicates  the 
presence  of  a  molecular  species  other  than  the  sodium  atom  in  these 
solutions.  While  similar  molecular  weight  determinations  have  not  been 
carried  out  in  solutions  of  metals  other  than  sodium,  nevertheless,  in 
view  of  the  similarity  of  the  properties  of  solutions  of  the  different  metals 
in  ammonia,  it  is  highly  probable  that  the  state  of  these  metals  differs 
little  from  that  of  sodium. 

3.  Material  Effects  Accompanying  the  Current.  The  criterion  for 
determining  whether  a  given  substance  is  a  metallic  or  an  electrolytic 
conductor  is  the  absence  or  existence  of  material  effects  accompanying 
the  passage  of  the  current.  In  dilute  solutions  of  the  metals  in  liquid 


SYSTEMS  INTERMEDIATE 


ammonia,  it  has  been  definitely  established  that  material  effects  accom- 
pany the  current  through  these  solutions.  The  existence  of  such  effects 
is  readily  observed  as  a  consequence  of  the  characteristic  color  of  these 
solutions.  If  a  current  is  passed  between  two  platinum  electrodes  in 
dilute  solution  of  sodium  or  potassium  in  liquid  ammonia,  it  is  found 
that  the  color  in  the  immediate  neighborhood  of  the  cathode  is  intensi- 
fied. This  result  is  obviously  due  to  the  fact  that,  as  the  current  passes 
through  the  solution,  the  metallic  element  as  an  ion,  either  simple  or 
complex,  is  carried  up  to  the  cathode.  The  electrolytic  character  of  the 


4" 


«• 


If 

94 


7.9    o-o    0.1    c.e    0.3   0.4   o.s    o.e  on    0,9   0.9    1.6    u     i.i     /.s 
Log  V. 

FIG.  63.    Apparent  Molecular  Weight  of  Sodium  in  Liquid  Ammonia  at  Different 

Concentrations. 


conduction  process  in  dilute  solutions  of  these  metals  in  liquid  ammonia 
is  therefore  established;  the  metal  is  associated  with  the  positive  ion. 
Taking  into  consideration  the  great  tendency  of  the  alkali  metals  to 
act  as  positive  ions,  it  is  probable  that  in  these  solutions  the  metals  are 
present,  in  part  at  least,  as  charged  atoms  which  do  not  differ  from  the 
positive  ions  of  salts  of  the  same  metals  dissolved  in  the  same  solvent. 
If  positive  ions  are  present  in  these  solutions,  then,  obviously,  nega- 
tive ions  must  be  present  likewise.  So  far  as  may  be  observed,  when  a 
current  passes  through  a  solution  of  a  metal  dissolved  in  liquid  ammonia, 
no  material  effect  occurs  at  the  anode,  save  that  the  concentration  of 
the  metal  in  the  immediate  neighborhood  of  this  electrode  is  diminished. 


370        PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

In  dilute  solutions,  this  effect  is  very  pronounced  and,  in  the  immediate 
neighborhood  of  the  anode,  the  solvent  appears  to  be  completely  freed 
from  the  metal,  since  the  solution  becomes  colorless  and  transparent. 
No  reaction  of  any  kind  appears  to  take  place  at  the  anode  surface,  no 
gas  is  evolved,  nor  is  any  manner  of  deposit  observable.    On  subjecting 
a  solution  of  sodium  in  ammonia  contained  in  a  U-shaped  tube  to  ex- 
tended electrolysis,  the  metal  may  be  completely  removed  from  the 
anode   limb   and   transferred   to  the   immediate   neighborhood   of   the 
cathode  surface.    In  this,  no  actual  loss  of  the  metal  occurs,  since  on 
reversing  the  current,  or  on  mixing  the  solution  by  shaking,  the  original 
solution  is  reproduced.    Apparently,  therefore,  there  is  present  in  these 
.  solutions  a  negative  carrier  whose  passage  into  the  anode  leaves  behind 
it  no  observable  material  effect.    The  nature  of  the  phenomenon  is  not 
appreciably  altered  if  another  metal  is  employed  in  place  of  sodium. 
We  commonly  associate  the  characteristic  metallic  properties  of  a 
substance  with  the  atoms  of  this  substance;  and,  in  the  case  of  com- 
pounds, we  associate  metallic  properties  with  the  electropositive  con- 
stituent.   A  brief  consideration,  however,  will  serve  to  show  that  this 
conception  is  erroneous,  and  that  the  electropositive  constituent  of  a 
compound  is  entirely  nonmetallic  in  its  character.    The  metals  owe  their 
characteristic  metallic  properties,  not  to  the  electropositive  constituent 
present,  but,  rather,  to  a  common  electronegative  constituent.     If  a  solu- 
tion of  potassium  in  liquid  ammonia,  which  has  a  characteristic  color, 
is  placed  between  two  solutions  of  potassium  amide,  which  are  trans- 
parent, then,  on  passing  a  current  through  this  system  of  solutions,  the 
motion  of  the  color  indicates  the  direction  in  which  the  free  metal  is 
transported  under  the  action  of  the  current.    If  the  characteristic  prop- 
erties of  a  solution  of  potassium  in  ammonia  were  due  primarily  to  the 
presence  of  an  electropositive  constituent,  then  we  should  expect  that 
the  color  would  move  toward  the  cathode.    It  has  been  found,  however, 
that,  actually,  under  these  conditions,  the  color  moves  toward  the  anode. 
As  has  been  shown,  potassium  in  liquid  ammonia  solutions  is  associated 
with  the  cation  and  moves  toward  the  cathode.     It  follows  that  the 
transfer  of  the  free  metal  in  the  solution,  placed  between  the  two  solu- 
tions of  potassium  amide,  is  effected  by  means  of  the  negative  carrier. 
In  passing  a  current  through  a  system  of  the  type  described  above,  there 
is  no  indication  that  anything  takes  place  as  the  positive  ions  pass  from 
the  potassium  solution  into  the  solution  of  potassium  amide,  save  that 
the  color  boundary  gradually  moves  in  a  direction  opposite  to  that  of 
the  positive  current,  that  is,  toward  the  anode.    It  is  probable,  there- 
fore, that  the  positive  ion  in  a  solution  of  metallic  potassium  in  liquid 


SYSTEMS  INTERMEDIATE  371 

ammonia  is  identical  with  the  positive  ion  of  a  solution  of  potassium 
amide  in  this  solvent.  In  other  words,  there  is  present  in  a  solution  of 
metallic  potassium  a  positive  carrier  identical  with  the  positive  carrier 
in  potassium  amide. 

The  positive  carrier,  then,  in  a  solution  of  a  metal  in  liquid  ammonia, 
is  nothing  other  than  the  normal  ion  of  this  metal  and  its  properties  in 
the  metal  solution  differ  in  no  wise  from  its  properties  in  a  solution  of 
its  salts.  On  the  other  hand,  it  is  evident  that,  as  the  negative  carrier 
moves  toward  the  anode  from  the  potassium  solution  to  the  potassium 
amide  solution,  free  metallic  potassium,  that  is,  metallic  potassium  not 
chemically  combined,  is  carried  in  the  direction  of  the  negative  current 
toward  the  anode.  The  metallic  properties  of  the  solutions  of  the  alkali 
metals  in  ammonia,  therefore,  must  be  due,  primarily,  to  the  negative 
carrier,  and  since  free  metallic  potassium  is  present  in  that  portion  of 
the  solution  where  blue  color  is  present,  it  follows  that  this  metal  is 
generated  by  interaction  between  the  potassium  ion  of  the  potassium 
amide  solution  and  the  negative  carrier  present  in  the  solution  of  metallic 
potassium  which,  under  the  action  of  the  potential  gradient,  moves  into 
the  potassium  amide  solution.  This  negative  carrier,  which  in  all  like- 
lihood is  identical  with  the  negative  electron,  is  the  essential  metallic 
constituent  of  metallic  substances. 

There  evidently  exists  in  a  metal  solution  an  equilibrium  of  the  type 

M+  +  e-  =  Me, 

where  M+  is  the  metallic  ion,  e~  is  the  negative  ion  (negative  electron) 
and  Me  is  the  neutral  metallic  atom.  In  the  amide  solution,  as  is  well 
known,  there  exists  an  equilibrium  according  to  the  equation: 

M+  +  NH2-  =  MNH2. 

It  is  evident  that,  as  the  negative  carrier  e~  is  carried  into  the  metal 
amide  solution,  equilibrium  establishes  itself  between  this  carrier  and  the 
other  molecular  species  present.  In  other  words,  the  reaction  takes  place: 


The  total  amount  of  free  metal  in  the  solution  at  any  time  is  e~  +  Me. 
To  what  extent  the  metal  atoms  are  ionized  into  normal  positive  ions 
and  negative  electrons  will  appear  below. 

4.  The  Relative  Speed  of  the  Carriers  in  Metal  Solutions.  If  the 
conduction  process  in  metals  consists  essentially  in  a  transfer  of  charge 
due  to  the  motion  of  the  negative  carriers,  since  no  material  effects  are 
observable  at  the  boundaries  between  different  metallic  conductors,  it 


372        PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

follows  that  the  negative  carrier  in  all  metals  is  the  same.  If  this  is 
true,  and  if  the  negative  carrier  in  the  solutions  of  the  alkali  metals  in 
ammonia'  is  the  negative  electron,  then  those  properties  of  these  solu- 
tions which  depend  upon  the  negative  carrier  should  be  the  same  in 
solutions  of  different  metals.  In  how  far  this  is  true  we  shall  see  pres- 
ently, since  many  of  the  properties  of  these  solutions  have  been  analyzed 
in  terms  of  their  ionic  constituents. 

Since  the  solutions  of  the  metals  in  ammonia  are  ionized,  the  prob- 
lem of  determining  the  nature  of  the  conduction  process  may  be  attacked 
in  a  manner  similar  to  that  employed  in  the  case  of  ordinary  electrolytic 
solutions.  It  is  possible,  in  the  first  place,  to  determine  the  relative 
amount  of  the  current  carried  by  the  two  ions  under  given  conditions. 
For  this  purpose,  transference  measurements  might  be  carried  out',  the 
concentration  changes  resulting  when  a  given  quantity  of  electricity 
passes  through  the  solution  being  determined.  This  experiment  is  diffi- 
cult of  execution,  and  consequently  recourse  has  been  had  to  another 
method,  the  results  of  which,  although  they  are  not  as  conclusive  as 
direct  transference  determinations,  nevertheless  make  it  possible  to 
determine  the  general  order  of  magnitude  of  the  quantities  involved.  The 
electromotive  force  of  a  concentration  cell  with  liquid  junction  is  given 
by  the  equation: 


from  which  the  value  of  n,  the  transference  number,  may  be  determined, 
if  the  electromotive  force  E  and  the  concentrations  C±YI  and  C2J2  are 
known  and  if  the  laws  of  dilute  solutions  are  applicable.  Judging  by  the 
results  obtained  in  solutions  of  ordinary  electrolytes,  this  equation  yields 
results  which  are  approximately  correct.  In  the  case  of  a  concentration 
cell  which  consists  of  two  platinum  electrodes  placed  in  metal  solutions, 
having  concentrations  C±  and  C2,  the  work  is  due  to  the  transfer  of  n 
mols  of  sodium  per  equivalent  of  electricity  from  the  concentration  Cx 
to  the  lower  concentration  C2.  The  cell  is  similar  to  that  of  a  salt  solu- 
tion with  reversible  anodes,  n  is  obviously  the  fraction  of  the  current 
transported  by  the  positive  carrier  in  the  solutions. 

In  Table  CXLIX  are  given  values  of  the  electromotive  force  of  con- 
centration cells  at  different  concentrations  —  the  rdtio  of  the  concentra- 
tions of  the  two  solutions  was  approximately  1:2  —  together  with  the 

transference  number  n  of  the  cation  and  the  ratio         n  . 

n 


SYSTEMS  INTERMEDIATE  373 

TABLE  CXLIX. 

E.M.F.  OF  CONCENTRATION  CELLS  AND  VALUES  OF  n  AND FOB 

SOLUTIONS  OF  Na  IN  NH3. 

Ca  EX103  n  1-^ 

0.870  0.080  0.00359  277.6 

0.732  0.328  0.0109  90,6 

0.335  0.620  0.0231  41.2 

0.164  0.72  0.0291  33.4 

0.081  0.86  0.0336  28.8 

0.040  1.07  0.0385  25.0 

0.020  1.38  0.0575  16.4 

0.010  1.80  0.0704  13.2 

0.005  2.60  0.0980  9.2 

0.0024  3.40  0.125  7.0 

In  Figure  64  are  shown  values  of  the  ratio  ;  in  other  words,  the 

n 

ratio  of  the  charge  transported  by  the  negative  carrier  to  that  transported 
by  the  positive  carrier.  On  examining  the  table,  it  will  be  seen  that,  for  a 
given  concentration  ratio,  the  electromotive  force  increases  as  the  con- 
centration decreases.  At  higher  concentrations,  the  electromotive  force 
decreases  very  rapidly  with  increasing  concentration  and  ultimately  be- 
comes extremely  small.  Referring  to  the  figure,  it  is  seen  that  at  low 
concentrations  the  ratio  of  the  carrying  capacities  of  the  two  ions  ap- 
proaches a  limiting  value;  that  of  the  negative  carrier  being  approxi- 
mately seven  times  that  of  the  positive  carrier.  As  the  concentration 
increases,  the  relative  amount  of  current  carried  by  the  negative  carrier 
increases,  at  first  slowly  and  then  more  and  more  rapidly.  In  the  neigh- 
borhood of  normal  concentration,  the  current  carried  by  the  negative 
carrier  is  several  hundred  times  as  great  as  that  carried  by  the  positive 
carrier.  As  we  have  seen,  the  positive  carrier  in  a  sodium  solution  is  in 
all  likelihood  identical  with  the  positive  ion  of  a  sodium  salt.  As  Frank- 
lin and  Cady  have  shown,  the  speed  of  this  ion  varies  only  little  with 
concentration.  The  increased  carrying  capacity  of  the  negative  ion  at 
higher  concentrations  must,  then,  be  due  to  an  increase  in  the  mean 
speed  of  the  negative  carriers. 

It  is  a  noteworthy  fact  that  the  carrying  capacity  of  the  negative 
carrier  in  dilute  solutions  is  much  greater  than  that  of  the  sodium  ion. 
The  speed  of  the  negative  carriers  in  these  solutions  must  therefore  be 
much  greater  than  that  of  the  sodium  ion.  The  speeds  of  the  different 


374        PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 


ions  of  salts  in  ammonia  solution,  as  we  have  seen,  do  not  differ  greatly. 
This  indicates  that  the  negative  carrier  in  the  metal  solutions  is  of  rela- 
tively small  dimensions.  '  Nevertheless,  if  the  negative  carrier  in  these 
solutions  were  the  negative  electron  unassociated  with  matter,  we  should 
expect  a  much  greater  value.  It  is  known,  however,  that,  owing  to  elec- 
trostatic action,  a  charge  placed  in  a  fluid  medium  tends  to  condense 
about  it  an  atmosphere  of  the  surrounding  molecules.  In  gases  at  higher 
pressures,  the  speed  of  the  negative  carrier  is  as  low  as,  and  often  lower 


300 


sso 


200 


too 


SO 


o.o 


o.s 


t.s 

Log  F. 


2.0 


3.0 


FIG.  64.    Relative  Speed  of  the  Negative  and  Positive  Ions  of  Sodium  in  Liquid 
Ammonia  at  Different  Concentrations. 

than,  that  of  the  positive  carrier  and  it  is  only  at  low  pressures  that  the 
negative  carrier  in  gases  loses  its  envelope  of  surrounding  molecules 
and  acquires  a  high  speed.  It  is  not  surprising,  therefore,  that  the  nega- 
tive electron  in  liquid  ammonia  should  possess  a  speed  comparable  with 
that  of  ordinary  ions.  At  higher  concentrations,  however,  as  is  indicated 
by  the  increased  carrying  capacity  of  the  negative  ion,  the  size  of  the 
surrounding  envelope  evidently  diminishes  and,  indeed,  it  has  been  shown 
that  some  of  the  negative  carriers  are  completely  unassociated  with 
ammonia. 

If  the  negative  carriers  are  associated  with  ammonia,  then  obviously, 


SYSTEMS  INTERMEDIATE  375 

due  to  the  motion  of  this  carrier,  ammonia  will  be  carried  from  the 
dilute  to  the  concentrated  solution.  If  the  vapor  pressures  of  the  two 
solutions  are  known,  we  may  calculate  the  work  due  to  the  transfer 
of  solvent  by  the  negative  carrier,  the  number  of  molecules  of  ammonia 
associated  with  this  carrier  being  assumed.  The  complete  expression 
for  the  electromotive  force  is: 

_      2nRT  .      M* 


where  m  is  the  number  of  molecules  of  ammonia  associated  with  the 
negative  carrier  and  p2  and  pv  are  the  vapor  pressures  of  the  two  solu- 
tions. If  we  place  n  =  0  in  this  equation,  that  is,  if  we  assume  that 
all  the  current  is  carried  by  the  negative  carriers,  we  may  calculate  a 
maximum  value  for  m,  if  the  electromotive  force  of  the  cell  and  the 
vapor  pressures  of  the  solutions  are  known.  For  a  concentration  cell 
between  solutions  whose  concentrations  were  1.014  and  0.627  normal,  the 
measured  electromotive  force  was  0.08  X  10'3  volts,  and  the  ratio  of  the 
vapor  pressures  was  1/1.006.  This  yields  for  m  the  value  0.67;  that  is, 
a  value  less  than  unity.  Since  m  cannot  be  less  than  unity,  it  follows 
that  at  least  a  portion  of  the  current  must  be  carried  by  carriers  not 
associated  with  ammonia.  It  is  evident,  from  the  manner  in  which  the 
electromotive  force  and  the  vapor  pressure  of  ammonia  solutions  vary 
with  the  concentration,  that  at  higher  concentrations  the  value  calculated 
for  m  would  be  even  smaller.  The  negative  carriers  in  solution,  there- 
fore, consist  of  negative  electrons  surrounded  with  ammonia  molecules. 
As  the  concentration  of  the  solution  increases,  the  number  of  ammonia 
molecules  associated  with  the  carriers  decreases  and  ultimately  a  por- 
tion of  the  carriers  becomes  entirely  free  from  ammonia  molecules.  The 
great  increase  in  the  relative  carrying  capacity  of  the  negative  carriers 
at  higher  concentrations  is  due  to  the  presence  of  these  free  negative 
electrons. 

5.  Conductance  of  Metal  Solutions.  If  the  increased  carrying 
capacity  of  the  negative  carrier  is,  in  fact,  due  to  an  increase  in  the 
mean  speed  of  this  carrier,  the  speed  of  the  positive  carrier  remaining 
substantially  constant,  then  the  equivalent  conductance  of  solutions  of 
the  metals  in  liquid  ammonia  should  increase  largely  with  the  concentra- 
tion at  higher  concentrations.  Since  the  determinations  of  the  molecular 
weight,  as  well  as  the  results  on  the  motion  of  the  boundary  between  a 
metal  and  a  metal  amide  solution,  indicate  that  an  equilibrium  exists 
between  the  positive  ions  and  the  negative  carriers  and  the  neutral 
atoms,  it  is  to  be  expected  that  the  ionization  of  the  metal  will  vary  as  a 


376        PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

function  of  the  concentration.  According  to  these  views  the  state  of  a 
metal  dissolved  in  ammonia  does  not  differ  materially  from  that  of  a 
salt  of  the  same  metal  dissolved  in  this  solvent.  The  only  material  dif- 
ference lies  in  the  fact  that,  whereas  in  the  metal  solution  the  negative 
electron  functions  as  negative  carrier,  in  the  salt  solution,  a  negative 
ion,  that  is,  a  negative  electron  attached  to  an  atomic  complex,  serves 
as  negative  carrier.  We  should  therefore  expect  the  equivalent  con- 
ductance in  dilute  solutions  to  vary  as  a  function  of  the  concentration 
in  a  manner  similar  to  that  of  normal  electrolytes.  In  other  words,  with 
decreasing  concentration  of  the  solution,  the  equivalent  conductance 
should  increase  and  approach  a  limiting  value. 

In  Table  CL  are  given  values  of  the  equivalent  conductance  of  solu- 
tions of  sodium  in  liquid  ammonia  at  its  boiling  point  at  different  con- 
centrations. The  density  of  the  solutions  not  being  known,  the  dilu- 
tions given  under  the  column  headed  V  represent  the  number  of  liters  of 
pure  ammonia  of  density  0.674,  in  which  one  atom  of  sodium  is  dis- 
solved. In  the  more  concentrated  solutions  the  density  is  considerably 
lower  than  that  of  pure  ammonia. 

TABLE  CL. 

CONDUCTANCE  OF  SODIUM  IN  AMMONIA  AT  — 33.50.5 

FA  FA 

0.5047  82490.  13.86  478.3 

0.6005  44100.  30.40  478.5 

0.6941  23350.  65.60  540.3 

0.7861  12350.  146.0  650.3 

0.8778  7224.  318.6  773.4 

0.9570  4700.  690.1  869.4 

1.038  3228.  1551.0  956.6 

1.239  2017.  3479.0  988.6 

2.798  749.4  7651.0  1009.0 

6.305  554.7  17260.0  1016.0 

37880.0  1034.0 

In  Figure  65  the  upper  curve  represents  the  equivalent  conductance  as 
a  function  of  log  V  up  to  a  concentration  of  approximately  normal.  From 
an  inspection  of  the  table  and  the  accompanying  figure,  it  will  be  seen 
that  the  conductance  curve  exhibits  a  minimum  in  the  neighborhood  of 
0.05  N.  At  lower  concentrations  the  equivalent  conductance  increases 
as  the  concentration  decreases  and  approaches  a  limiting  value  in  the 
neighborhood  of  1016.  The  form  of  the  curve  at  these  concentrations  is 

•Kraus,  loc.  cit. 


SYSTEMS  INTERMEDIATE 


377 


similar  to  that  of  binary  electrolytes  in  liquid  ammonia,  the  only  ma- 
terial difference  being  that  the  conductance  has  a  much  higher  value. 
The  equivalent  conductance  of  the  sodium  ion  is  130.  It  follows,  then, 
that  the  equivalent  conductance  of  the  negative  carrier  in  these  solutions 
at  low  concentrations  is  in  the  neighborhood  of  X886,  or  6.8  times  that  of 
the  sodium  ion.  We  saw  in  the  previous  section  that  the  results  of 
measurements  of  the  electromotive  force  of  concentration  cells  indicate 
that  the  carrying  capacity  of  the  negative  carrier  is  approximately  7 
times  that  of  the  positive  ion  in  a  sodium  solution.  This  value,  therefore, 
is  in  excellent  agreement  with  the  value  6.8  obtained  from  conductance 


Equivalent  Conductance, 
Lower  Curve. 

-!  *  !  -*  s 
!  !  I  !  I 

1 

\ 

^ 

f  ' 

*• 

1 

1 

\ 

/ 

V 

V 

*-%•  —  f 

X 

O 
Q 


l.s        0.0        o.s         /.o         /.s         *&        t.s        a.o        js        +.0       *.*• 

Log  V. 

FIG.  65.     Equivalent  Conductance  of  Sodium  in  Liquid  Ammonia  at  — 33.5°    at 

Different  Concentrations. 

measurements.  Evidence  has  already  been  presented  which  indicates 
that  the  positive  ion  in  a  sodium  solution  is  identical  with  the  positive 
ion  in  a  solution  of  a  sodium  salt.  The  fact  that  the  conductance  of  the 
positive  ion,  as  derived  from  measurements  with  the  metal  solutions, 
corresponds  with  that  of  the  sodium  ion  as  derived  from  measurements 
with  solutions  of  sodium  salts  confirms  this  hypothesis.  The  positive 
ion  in  a  solution  of  sodium  in  liquid  ammonia  is  therefore  the  normal 
sodium  ion. 

If,  now,  we  examine  the  conductance  curve  in  the  more  concentrated 
solutions,  we  see  that  below  a  concentration  of  0.05  N  the  conductance 
increases  with  the  concentration,  the  increase  being  the  greater  the 
higher  the  concentration.  This,  again,  confirms  the  conclusion  derived 
from  a  study  of  the  electromotive  force  of  concentration  cells.  As  the 
concentration  increases,  the  relative  carrying  capacity  of  the  negative 
carrier  increases.  The  increase  in  conductance  is  due  to  an  increase  in 
the  mean  speed  of  this  carrier,  since  at  higher  concentrations  the  con- 


378        PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

ductance  increases  enormously,  which  result  may  be  accounted  for  only 
on  the  assumption  that  the  speed  of  one  or  both  of  the  carriers  increases. 
Since  one  of  these  carriers  is  the  normal  sodium  ion,  it  follows  that  the 
conductance  is  due  to  an  increase  in  the  speed  of  the  negative  carrier. 
If  these  conclusions  are  valid,  then,  at  high  concentrations,  the  conduc- 
tance of  the  metal  solutions  should  approach  that  of  the  metals  them- 
selves, for  at  high  concentrations  the  number  of  carriers  and  negative 
electrons  present  in  the  solution  becomes  comparable  with  that  of  the 
total  number  of  molecules  present,  in  which  case  we  should  expect  that 
a  considerable  fraction  of  these  carriers  would  be  free  from  ammonia 
molecules.  This  is  borne  out  by  the  results  of  conductance  measure- 
ments. As  may  be  seen  from  Table  CL,  the  equivalent  conductance  in- 
creases from  a  value  of  approximately  475  at  a  concentration  of  0.05  N 
to  a  value  of  approximately  2000  at  normal  and  to  approximately  82000 
at  a  concentration  of  2  normal.  At  this  concentration  the  specific  con- 
ductance of  the  solution  is  163.5,  the  specific  conductance  of  mercury 
being  1.063X10*,  which  is  about  six  times  that  of  the  metal  solution  at 
the  concentration  in  question.  The  lower  curve  in  Figure  65  shows  how 
the  conductance  varies  with  concentration  up  to  2  N. 

In  the  following  table  are  given  values  of  the  specific  conductance  of 
solutions  of  sodium  in  liquid  ammonia  up  to  the  saturation  point  of  these 
solutions.6 

TABLE   CLI. 

SPECIFIC  CONDUCTANCE  OF  CONCENTRATED  SOLUTIONS  OF  SODIUM 
IN  AMMONIA  AT  — 33.5°. 

V  n  V  \i 

0.1081  5047.0  0.5099  148.3 

0.1331  4954.0  0.7612  20.21 

0.1804  2687.0  0.9265                 5.988 

0.2768  1070.0  1.298                   1.269 

0.3230  714.0  1.674                  0.6465 

The  results  for  sodium,  together  with  those  for  potassium,  are  shown 
graphically  in  Figure  66,  where  the  logarithms  of  the  specific  conduc- 
tance are  plotted  against  the  logarithms  of  the  dilution  V  as  defined 
above.  The  curve  passing  through  the  points  is  that  of  potassium;  the 
other,  that  of  sodium.  At  the  highest  concentrations,  the  solutions  were 
saturated,  so  that  the  specific  conductance  was  independent  of  the  total 
amount  of  ammonia  present.  The  second  point  for  the  value  V  =  0.1331 

•Kraus  and  Lucasse,  J.  Am.  Chem.  Soc.  }3  (Dec.,  1921). 


SYSTEMS  INTERMEDIATE 


379 


lies  just  below  the  saturation  point.  The  specific  conductance  of  the 
saturated  solution  is  0.5047  X  104;  or,  almost  precisely  one  half  that  of 
mercury  at  0°.  That  the  solutions  of  the  metals  in  liquid  ammonia  at 
these  concentrations  are  metallic  admits  of  no  doubt.  They  exhibit  all 
the  properties  of  metallic  substances,  both  optical  and  electrical.  A 
brief  consideration  will  show,  indeed,  that  in  these  solutions  the  metal 
possesses  an  exceptionally  high  conducting  power  compared  with  that  of 


3.0 


CQ 


I 


o.s 


o.o 


7.S 


l.o 


2.9     To      T.Z     74-      7*6      7.B     0.0     o.a.     0.4-    o.e     o.& 
Log  V. 

FIG.   66.    Conductance    of    Concentrated    Solutions    of   Sodium   and   Potassium    in 
Liquid  Ammonia  at  — 33.5°. 

many  metals.  Obviously,  if  metallic  conduction  is  due  to  the  motion  of 
charged  carriers,  then  two  factors  influence  the  conductance;  in  the  first 
place,  the  resistance  which  the  carriers  experience  in  their  motion,  and, 
in  the  second,  the  number  of  carriers  present  in  a  given  volume.  In 
comparing  the  conducting  power  of  different  metals,  it  is  not  sufficient 
to  merely  compare  their  specific  conductances.  The  concentration  factor 
should  also  be  taken  into  account.  If  the  specific  conductance  is  divided 
by  the  number  of  gram  atoms  per  cubic  centimeter,  the  ratio  yields  the 
atomic  conductance  of  the  metal.  The  atomic  conductance  of  a  satu- 


380        PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 


rated  solution  of  sodium  in  ammonia 6a  is  1.1  X  106  The  atomic  con- 
ductance of  metallic  sodium  at  room  temperatures  is  5.05  X  106.  The 
conductance  of  the  saturated  solution  is  therefore  comparable  with  that 
of  the  pure  metal.  Values  of  the  atomic  conductance  of  other  metals  will 
be  found  in  Table  CLIII  of  the  next  chapter.  The  atomic  conductance  of 
sodium  solutions  is  about  the  same  as  that  of  osmium  and  tin  and  much 
greater  than  that  of  mercury  (liquid)  and  bismuth. 


400 


0,0 


3.0 


4.0 


2.0 

Log  V. 

FIG.  67.    Conductance  of  Dilute  Solutions  of  Potassium ,  and  Lithium  and  of  Mix- 
tures of  Sodium  and  Potassium  in  Liquid  Ammonia  at  — 33.5°. 

The  view  was  expressed,  above,  that  the  negative  carrier  for  dif- 
ferent metals  dissolved  in  liquid  ammonia  is  the  same  and  is,  in  fact,  the 
negative  electron,  which  carrier  presumably  effects  the  passage  of  the 
current  through  all  metallic  substances.  If  this  view  is  correct,  then,  at 
higher  concentrations,  where  the  conductance  of  the  solution  is  due 
almost  entirely  to  the  negative  electron,  solutions  of  different  metals  in 
ammonia  should  exhibit  very  nearly  the  same  properties.  It  is  to  be 

••  This  is  based  on  the  value  0.54  for  the  density  of  the  saturated  solution  as  deter- 
mined approximately  by  Dr.  Lucasse  in  the  Author's  Laboratory.  This  value  may  be  in 
error  by  several  per  cent. 


SYSTEMS  INTERMEDIATE  .  381 

expected,  of  course,  that  minor  variations  will  be  observed,  since  equiva- 
lent solutions  are  not  physically  .identical.  The  densities  of  potassium 
and  sodium  solutions,  for  example,  differ;  and  the  amount  of  ammonia 
associated  with  the  positive  ions  in  these  solutions  doubtless  differs. 
Aside  from  minor  differences,  we  should  expect  those  properties  of  metal 
solutions,  which  depend  upon  the  negative  carrier,  to  be  relatively  inde- 
pendent of  the  nature  of  the  metal.  In  Figure  67  are  shown  the  conduc- 
tance curves  of  dilute  solutions  of  potassium,  lithium,  and  mixtures  of 
sodium  and  potassium.  The  uppermost  curve  is  that  of  potassium,  the 
lowest  that  of  lithium,  while  the  intermediate  curve  is  that  of  a  mixture 
of  sodium  and  potassium.  The  curve  for  mixtures  of  sodium  and  potas- 
sium lies  intermediate  between  that  of  sodium  and  of  potassium.  It  is 
seen  that  in  the  case  of  very  dilute  solutions  of  potassium  and  lithium, 
the  conductance  values,  as  shown,  lie  below  the  true  values  owing  to  the 
fact  that  these  metals  react  with  the  solvent  according  to  the  equation: 

Me  +  NH3  =  MeNH2  +  £H2; 

that  is,  the  metals  react  with  the  solvent  to  form  the  amides.  This  re- 
moves a  portion  of  the  metal  from  solution  and  consequently  the  con- 
ductance values  measured  are  lower  than  the  true  values.  From  the 
extensive  data  presented  by  Kraus,.  however,  there  can  be  no  doubt  as 
to  the  cause  for  the  low  values  observed  in  dilute  solutions  in  the  case 
of  potassium  and  lithium.  At  intermediate  concentrations,  where  the 
formation  of  amide  is  not  marked,  the  conductance  of  the  solutions 
diminishes  in  the  order:  potassium,  sodium,  lithium.  At  a  given  con- 
centration, the  difference  in  the  values  of  the  conductance  of  these 
metals  corresponds  approximately  to  the  difference  in  the  conductance 
of  the  positive  ions  of  these  metals.  This  shows  that  in  dilute  solutions 
of  potassium,  sodium  and  lithium  in  liquid  ammonia,  the  conductance  of 
the  negative  carrier  is  the  same ;  presumably,  therefore,  the  negative  car- 
riers are  identical  in  the  three  cases.  At  higher  concentrations,  where 
the  conductance  of  the  positive  ion  becomes  negligible  in  comparison 
with  that  of  the  negative  carrier,  we  should  expect  the  specific  conduc- 
tance of  the  solutions  to  be  practically  the  same  at  the  same  equivalent 
concentration.  As  may  be  seen  from  Figure  66,  the  conductance  curves 
for  sodium  and  potassium  possess  the  same  form,  and  over  a  considerable 
range  of  concentration  they  are  practically  identical.7  At  higher  con- 
centrations, slight  variations  occur  as  might  be  expected,  since  the  den- 
sities of  these  solutions  are  not  the  same.  The  conclusion  that  the 

T  Kraus  and  Lucasse,  loc.  tit. 


382       PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

negative  carrier  of  the  different  metals  is  the  same  appears,  therefore, 
amply  justified. 

The  temperature  coefficient  of  sodium  solutions  in  liquid  ammonia 
has  been  measured.  In  Table  CLII  are  given  values  of  the  resistance 
of  fairly  dilute  sodium  solutions  from  the  boiling  point  of  liquid  ammonia 
up  to  85°C.  In  the  last  column  are  given  values  of  the  mean  percentage 
temperature  coefficient  of  these  solutions  over  various  temperature  inter- 
vals referred  to  the  resistance  at  —  33°.7a 

TABLE    CLII. 

TEMPERATURE  COEFFICIENT  OF  DILUTE  SODIUM  SOLUTIONS. 

A(l/fl) 
t  R  X  * 


—  33°  124.3 

—  13°  85.7  2.25 
+  17°  43.4  4.69 
+  48°  28.2  5.34 
+  85°  15.6  9.00 

It  is  seen  that  at  low  temperatures  the  temperature  coefficient  of  the 
conductance  of  these  solutions  is  approximately  2  per  cent,  and  as  the 
temperature  increases  the  temperature  coefficient  increases  markedly 
reaching  a  value  of  9  per  cent  for  the  interval  between  45°  and  85°. 
This  behavior  of  the  metal  solutions  in  liquid  ammonia  is  in  striking 
contrast  to  that  of  normal  electrolytes  dissolved  in  this  solvent.  At 
ordinary  concentrations,  the  conductance  of  these  solutions  passes 
through  a  maximum  in  the  neighborhood  of  room  temperatures,  the 
conductance  decreasing  with  increasing  temperatures  above  this  point. 
It  is  obvious  that  the  factors  involved  in  the  temperature  coefficients  of 
the  metal  solutions  are  very  different  from  those  involved  in  solutions  of 
ordinary  electrolytes.  It  is  difficult,  in  the  present  state  of  our  knowl- 
edge, to  state  to  what  the  high  value  of  the  temperature  coefficient  is 
due.  However,  since  in  fairly  dilute  solutions  the  conductance  is  due 
primarily  to  the  negative  electron  more  or  less  associated  with  ammonia, 
it  is  possible  that  the  high  value  of  the  temperature  coefficient  at  higher 
temperatures  is  due  to  an  increase  in  the  mean  speed  of  the  negative 
carriers  as  a  result  of  a  diminution  in  the  size  of  the  solvent  envelope 
with  which  the  negative  electrons  are  surrounded. 

While  at  low  concentrations  the  temperature  coefficient  of  the  metal 

T*  Kraus,  loc.  cit. 


SYSTEMS  INTERMEDIATE  383 

solutions  is  greater  than  that  of  ordinary  electrolytes,  at  high  concen- 
trations the  temperature  coefficient  is  markedly  lower.8  At  a  dilution 
V  —  0.18,  the  temperature  coefficient  is  approximately  0.17%.  It  is 
evident  that  at  higher  concentrations  the  value  of  the  temperature  coef- 
ficient decreases  as  the  concentration  increases.  In  the  neighborhood  of 
the  saturation  point,  the  coefficient  is  not  far  from  zero,  and,  were  it 
possible  to  prepare  solutions  having  higher  concentrations,  it  might  be 
expected  that  the  temperature  coefficient  would  even  become  negative 
as  it  is  in  metals.8* 

These  data  on  the  temperature  coefficient  of  the  metal  solutions  in 
liquid  ammonia  serve  further  to  differentiate  these  solutions  from  solu- 
tions of  ordinary  electrolytes.  The  behavior  of  the  very  concentrated 
solutions  clearly  indicates  an  intimate  relation  between  these  solutions 
and  ordinary  metallic  conductors.  The  properties  of  the  metal  solutions 
in  liquid  ammonia,  therefore,  supply  abundant  evidence  to  the  effect 
that  conduction  in  metals  is  due  to  the  motion  of  a  negative  carrier  of 
sub-atomic  dimensions,  which  carrier  is  the  same  for  all  metals.  Since 
the  only  carrier  of  sub-atomic  dimensions  which  has  been  observed  is  the 
negative  electron,  we  may  infer  that  the  effective  carrier  in  metals,  as 
in  these  solutions,  is  the  negative  electron. 

8  Observations  by  Dr.  W.  W.  Lucasse  in  the  Author's  Laboratory. 

8»  Since  this  was  written,  the  temperature  coefficient  of  sodium  in  liquid  ammonia 
has  been  determined  by  Dr.  Lucasse  from  a  dilution  F  =  1.7  up  to  the  saturation  point 
The  coefficient  for  the  saturated  solution  is  0.067%.  As  the  concentration  decreases,  the 
temperature  coefficient  increases  decidedly  reaching  a  maximum  of  3.65%  at  V  =  1 06 
after  which  it  decreases  more  slowly,  falling  to  2.47%  at  V  =  1.7. 


Chapter  XV. 
The  Properties  of  Metallic  Substances. 

1.  The  Metallic  State.  With  the  exception  of  the  elements  of  the 
argon  group  and  the  strongly  electronegative  elements  of  lower  atomic 
weight,  elementary  substances  are  metallic.  Compounds  between 
strongly  electronegative  and  strongly  electropositive  elements,  as  well 
as  compounds  between  the  more  electronegative  elements,  are  non- 
metallic;  while  compounds  between  distinctly  metallic  elements  are 
throughout  metallic.  Compounds  between  the  less  strongly  electronega- 
tive elements  and  the  less  strongly  electropositive  elements  are  often 
metallic  in  the  solid  state.  Thus  the  compounds  of  the  alkali  metals 
and  the  metals  of  the  alkaline  earths  with  the  elements  of  the  halogen 
and  of  the  oxygen  groups  are  non-metallic;  while  compounds  of  the  less 
electropositive  elements,  such  as  lead  and  iron,  with  the  elements  of  the 
oxygen  group  are  often  metallic.  Within  this  class  are  also  included 
certain  free  electropositive  groups,  containing  both  metallic  and  non- 
metallic  elements,  and  possibly  groups  containing  only  nonmetallic 
elements.  Thus,  the  free  group  CH3Hg  is  metallic,1  while  certain  of 
the  substituted  ammonium  groups  form  stable  metallic  amalgams.12 
There  is  also  evidence  that  the  quaternary  substituted  ammonium  groups 
are  soluble  in  ammonia  in  the  free  state,  and  that  in  solution  their  prop- 
erties resemble  those  of  the  alkali  metals.3  The  property  of  metallicity, 
therefore,  is  not  to  be  looked  upon  as  an  atomic  property,  since  various 
groups  of  nonmetallic  elements  in  the  free  state  exhibit  metallic 
properties. 

The  metals  thus  comprise  a  major  portion  of  the  elementary  sub- 
stances and  a  large  number  of  compounds  between  metallic  and  non- 
metallic  elements.  While  nonmetallic  compounds  may,  in  a  large 
measure,  be  accounted  for  through  the  interaction  of  the  negative  elec- 
trons with  atoms,  a  similar  theory  of  the  constitution  of  metallic  com- 
pounds has  not  thus  far  been  developed.  One  of  the  remarkable  facts 

»Kraus,  J.  Am.  Chem.  Soc.  35,  1732  (1913). 

•McCoy  and  Moore,  J.  Am.  Chem.  Soc.  33,  273  (1911). 

•Palmaer,  Ztschr.  f.  Elelctroch.  8,  729  (1902)  ;  Kraus,  loc.  cit. 

384 


THE  PROPERTIES  OF  METALLIC  SUBSTANCES  385 

in  connection  with  inter-metallic  compounds  is  the  large  number  of 
compounds  derivable  from  a  single  pair  of  elementary  substances.  The 
constitution  of  these  compounds  does  not  harmonize  well  with  our  pres- 
ent conceptions  of  valence.  The  study  of  these  substances  is  attended 
with  many  experimental  difficulties  and  their  nature  at  the  present  time 
is  little  understood. 

Metallic  substances  are  characterized  by  certain  well-defined  prop- 
erties, chiefly  electrical  and  optical,  which  are  common  to  all.4  This 
community  of  property  among  metallic  substances  indicates  some  com- 
mon element  within  their  constitution.  During  the  past  few  decades  the 
view  has  been  gaining  ground  that  the  properties  of  metallic  substances 
are  primarily  due  to  the  presence  of  charged  particles,  presumably  nega- 
tive electrons,  which  are  relatively  free  to  move  within  the  body  of  the 
metal.  While  this  theory  of  the  constitution  of  metals  is  in  good  agree- 
ment with  observed  facts  from  a  qualitative  point  of  view,  it  has  not 
been  found  possible  to  elaborate  a  detailed  theory  of  metallic  substances 
which  accounts  successfully  for  the  major  portion  of  their  characteristic 
properties. 

2.  The  Conduction  Process  in  Metals.  Metallic  conductors  are  dif- 
ferentiated from  electrolytic  conductors  in  that  the  passage  of  the  cur- 
rent through  them  is  unaccompanied  by  an  appreciable  transfer  of  mat- 
ter. If  a  current  is  passed  for  an  indefinite  period  of  time  through  a 
series  of  metallic  conductors,  no  material  effects  are  observable,  either 
within  the  conductors  themselves  or  at  the  boundaries  between  them. 
If  the  conduction  process  in  metals  is  due  to  the  motion  of  negative 
electrons,  then  there  must  likewise  be  present  in  the  metals  positively 
charged  constituents  or  ions  which,  conceivably,  may  take  part  in  the 
conduction  process.  In  all  likelihood  the  amount  of  matter  transferred 
by  these  carriers  is  extremely  small,  and  may  under  ordinary  conditions 
escape  observation.  Experiments  carried  out  with  amalgams  of  sodium 
and  potassium  indicate  that  in  these  systems  an  appreciable  transfer  of 
matter  actually  takes  place.5  Curiously  enough,  in  these  amalgams,  the 
electropositive  constituent,  that  is,  the  alkali  metal,  was  found  to  be 
carried  toward  the  anode  and  not  toward  the  cathode  as  might  have 
been  expected.  The  data  are  as  yet  too  meager  to  warrant  drawing 

*  A  very  complete  summary  of  the  literature  relating  to  metallic  substances  is  given 

by  J.  Koenigsberger  in  Handbuch  d.  Elektrizitat  u.  d.  Magnetismus  by  L.  Graetz,  Leipzig 

J.   A.   Earth    (1920),   Vol.   3,    pp.   597-724.     The   older   literature   is   also   summarized   in 

Winkelmann's    Handbuch    d.    Physik,    Vol.    4,    pp.    344-384,    and    Baedeker's    Elektrische 

Erscheinungen  in  Metallischen  Leitern,  Vieweg,  Braunschweig  (1911). 

8  Lewis,  Adams  and  Lanman,  J.  Am.  Chem.  8oc.  37,  2656  (1915). 


386       PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

conclusions  as  to  the  part  which  the  positive  constituent  plays  in  metallic 
conduction.  It  appears  probable,  however,  that  in  suitable  metallic 
systems  an  appreciable  transfer  of  matter  accompanies  the  passage  of 
the  current. 

The  view  that  the  conduction  process  in  metals  is  an  ionic  one  is  the 
only  one  in  agreement  with  our  present  notions  regarding  the  constitu- 
tion of  matter.  The  absence  of  material  effects  accompanying  the  trans- 
fer of  electricity  indicates  a  common  carrier  in  all  metallic  substances. 
The  fact  that  no  positively  charged  carrier  of  sub-atomic  dimensions  is 
known  lends  probability  to  the  view  that  metallic  conduction  is  due  to 
the  motion  of  the  negative  electron,  the  only  known  carrier  of  sub-atomic 
dimensions. 

Direct  evidence  in  support  of  the  electron  theory  of  metallic  con- 
duction is  very  meager.  Tolman  and  Stewart 6  have  studied  the  current 
flow  induced  in  metallic  conductors  under  acceleration.  From  their  meas- 
urements, they  have  calculated  the  ratio  of  the  effective  mass  of  the 
carriers  to  the  quantity  of  electricity  flowing.  Their  results  indicate  that 
the  current  is  due  to  the  motion  of  a  negative  carrier,  the  ratio  of  whose 
mass  to  the  charge  corresponds  with  that  of  the  negative  electron.  For 
copper,  aluminum  and  silver  conductors,  Tolman  and  Stewart  found  for 
the  value  of  1/ra,  assuming  0  =  16,  the  values  1660,  1590,  and  1540 
respectively.  These  are  somewhat  lower  than  corresponds  to  the  mass 
of  a  slowly-moving  negative  electron,  but  the  difference  lies  within  the 
limits  of  experimental  error.  The  results  of  investigations  on  the  prop- 
erties of  solutions  of  the  alkali  metals  in  liquid  ammonia,  described  in 
the  preceding  chapter,  likewise  furnish  striking  evidence  in  support  of 
the  electron  theory  of  metallic  conduction.  Other  properties  of  the 
metals,  such  as  the  Hall  effect,  and  particularly  the  emission  of  negative 
electrons  by  metals  at  higher  temperatures,  lend  support  to  this  theory. 
The  precise  nature  of  the  conduction  process  of  metals,  however,  still 
remains  very  obscure. 

3.  The  Conductance  of  Elementary  Metallic  Substances.  The 
order  of  magnitude  of  the  conductance  of  metals,  in  itself,  furnishes 
evidence  in  support  of  the  electron  theory  of  metallic  conduction.  In 
Table  CLIII  are  given  values  of  the  atomic  conductance  and  the  spe- 
cific resistance,  as  well  as  of  the  mean  temperature  coefficient  a  of  the 
resistance  of  a  number  of  elementary  metals. 

•Tolman  and  Stewart,  Phys.  Rev.  8,  97  (1916)  ;  i?w?.,  9,  164   (1917), 


THE  PROPERTIES  OF  METALLIC  SUBSTANCES 


387 


TABLE   CLIII. 

ATOMIC  CONDUCTANCE,  SPECIFIC  RESISTANCE  AND  RESISTANCE  TEMPERA- 
TURE COEFFICIENT  OF  ELEMENTARY  METALS  AT  0°. 


Metal 


A  X  10-6 


Silver 6.999 

Potassium  6.503 

Sodium  :..  5.288 

Rubidium 4.845 

Copper   4.559 

Gold    4.547 

Caesium  3.898 

Aluminium 3.834 

Magnesium  3.215 

Chromium   2.989 

Calcium   2.457 

Indium   1.905 

Cadmium  1.875 

Rhodium    1.811 

Zinc 1.713 

Lithium 1.534 

Iridium 1.414 

Tantalum 1.339 

Tin 1.252 

Osmium    1.119 

Thallium  0.9775 

Nickel 0.9613 

Lead   0.9222 

Palladium 0.9082 

Platinum 0.8314 

Iron 0.8031 

Strontium    0.7194 

Cobalt 0.7064 

Manganese    0.6561 

Antimony 0.4658 

Arsenic  0.3735 

Gallium  0.2208 

Bismuth   0.1972 

Mercury  0.1564 


CTO  X  106 

1.468 
6.100 
4.28 
11.60 
1.561 
'  2.197 
18.12 
2.563 
4.355 
4.40 
10.50 
8.370 
10.023 
4.700 
5.751 
8.550 
8.370 
14.60 
13.048 
9.500 
17.633 
12.323 
20.380 
10.219 
11.193 
9.065 
24.75 
9.720 
4.400 
39.00 
35.10 
53.40 
108.00 
95.80 


Oo-100Xl03 

4.10 

5.5 

5.1 

4.33 
3.98 

4.26 
3.90 


4.74 

4.24 

4.43 

4.17 

4.57 

3.71 

3.47 

4.47 

4.2 

5.17 

4.87 

4.22 

3.77 

3.92 

6.57 

3.66 

4.73 
3.89 

4.46 
0.88 


As  may  be  seen  from  the  table,  the  specific  resistance  of  silver  is 
1.47  X  10'6.  Compared  with  this,  the  specific  resistance  of  fused  salts 
is  of  the  order  of  1.0  and  that  of  electrolytes,  at  normal  concentration,  10. 
In  comparing  the  conducting  power  of  metals  it  is  more  rational  to 
employ  the  atomic,  or  perhaps  even  the  equivalent,  rather  than  the  spe- 
cific conductance,  On  this  basis,  metallic  conductors  exhibit  many  rela.- 


388       PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

tionships  which  otherwise  are  not  apparent.7  The  atomic  conductance 
of  potassium  and  of  silver  is  of  the  order  of  6  X  106  and  that  of  mercury 
at  ordinary  temperatures,  which  is  a  relatively  poor  conductor,  1.5  X  105. 
Compared  with  these  values,  the  equivalent  conductance  of  fused  salts 
is  in  the  neighborhood  of  50  and  that  of  electrolytes  at  low  concentra- 
tions 100.  In  a  few  instances,  the  equivalent  conductance  of  electrolytes 
is  considerably  higher,  as,  for  example,  in  aqueous  solutions  at  high  tem- 
peratures, where  it  approaches  a  value  of  1000,  and  in  solutions  of  the 
alkali  metals  in  liquid  ammonia  at  low  concentrations.  The  above  values 
relate  to  the  conductance  of  metals  at  ordinary  temperatures.  If  a  simi- 
lar comparison  were  made  at  lower  temperatures,  the  relative  conduct- 
ingf  power  of  the  metals  would  be  found  to  be  enormously  greater.  The 
conductance  of  metals  at  very  low  temperatures  will  be  discussed  in 
the  next  section. 

The  conductance  of  elementary  metals  in  the  liquid  state  is,  in  gen- 
eral, lower  than  in  the  solid  state.  The  process  of  fusion  is  accompanied 
by  a  discontinuous  change  in  the  conductance  values.  In  the  following 
table  are  given  the  ratios  of  the  specific  conductances  \is  /^  of  metals 
in  the  solid  and  liquid  states,  together  with  the  ratio  of  their  specific 
volumes  Vi/vs. 

TABLE    CLIV. 

CHANGE  OF  THE  SPECIFIC  CONDUCTANCE  OF  ELEMENTARY  METALS 

ON  MELTING. 

Specific 
Conductance 
Melting  at  the 

Metal  Point  Melting  Point        Hs/ty          vl/vs 

Lithium. 177.8°  2.6  X  104  2.51 

Sodium    97.6  9.5  X  104  1.34  1.024 

Potassium 62.5  7.7  X  104  1.39  1.024 

Caesium. 26.4  2.54  X  104  1.65  1.027 

Zinc... 419.  2.7X104  2.0  >1 

Cadmium 321.  2.9  X  104  1.96  1.047 

Mercury    —38.8  1.10  X  104  4.1  1.036 

Thallium.. 301.  1.35  X  104  2.0 

Tin   232.  2.1  X  104  2.2  1.028 

Lead 327.  1.06  X  104  1.95  1.034 

Antimony   629.5  0.88  X  104  0.70 

Bismuth 269.  0.78  X  104  0.46  0.967 

7  Richarz,  Zfschr.  }.  anorp.  Chew.  50,  356   (1908)  ;  Benedicks,  JaJirb.  f.  Ro4,  IS,  351 


THE  PROPERTIES  OF  METALLIC  SUBSTANCES  389 

As  may  be  seen  from  the  table,  expansion  of  the  metal  on  melting  is,  in 
general,  accompanied  by  an  increase  of  resistance.  The  change  in  the 
specific  conductance  is  particularly  marked  in  the  case  of  mercury.  In 
the  case  of  antimony  and  bismuth,  the  specific  conductance  increases  on 
fusion.  This  is  particularly  marked  in  the  case  of  bismuth,  which 
expands  on  fusion. 

A  change  in  state  of  an  elementary  metal  is  at  times  accompanied  by 
a  discontinuous  change  in  the  conductance  values  and  at  times  only  by 
discontinuity  in  the  temperature  coefficient.  The  transition  from  gray 
tin  to  ordinary  tin  is  doubtless  accompanied  by  a  discontinuous  change 
in  resistance,  although  the  specific  conductance  of  gray  tin  appears  not 
to  have  been  determined.  In  the  case  of  elementary  metals  of  very  low 
conducting  power,  such  as  metallic  silicon,  discontinuous  changes  in  the 
conductance  curve  have  been  observed.  In  other  cases,  as,  for  example, 
the  transition  of  the  magnetic  metals  at  the  recalescence  point,  the  resist- 
ance curve  itself  is  continuous,  but  the  temperature  coefficient  under- 
goes a  discontinuous  change,  as  we  shall  see  below. 

4.  The  Conductance  of  Elementary  Metals  as  a  Function  of  Tem- 
perature. The  electrical  properties  of  different  solid  elementary  metals 
are  strikingly  similar.  With  increasing  temperature,  the  resistance  of 
elementary  metals  increases,  the  mean  coefficient  having  a  value  in  the 
neighborhood  of  0.004,  which  does  not  differ  greatly  from  the  coefficient 
of  expansion  of  gases  at  low  pressures.  Certain  metals,  as,  for  example, 
the  magnetic  metals  iron  and  nickel,  have  coefficients  much  higher  than 
this  value,  particularly  at  higher  temperatures.  The  resistance  of  most 
metals  increases  approximately  as  a  linear  function  of  the  temperature, 
and  over  larger  temperature  ranges  the  resistance  may  be  expressed  very 
nearly  as  a  function  of  the  temperature  by  means  of  a  quadratic 
equation. 

With  decreasing  temperature,  the  resistance  of  pure  metals  decreases 
and,  down  to  liquid  air  temperatures,  it  would  appear  that  a  value  of 
zero  is  being  approached  as  a  limit  at  the  absolute  zero.  The  experi- 
ments of  Kammerlingh  Onnes  at  liquid  helium  temperatures,  however, 
have  brought  to  light  the  remarkable  fact  that  at  very  low  temperatures 
the  resistance  of  pure  metals  undergoes  a  discontinuous  change.  When 
a  certain  temperature  is  reached,  the  resistance  falls  off  abruptly  to 
values  which  are  almost  negligible,  if  not  actually  zero.8  For  example, 
at  4.24°  K.  the  resistance  of  mercury  in  terms  of  its  value  at  0°  (extrapo- 

•  Kammerlingh  Onnes,  numerous  papers  in  the  Proceedings  of  the  KoninklHkP  Ak*»/i 
emie  van  Wetenschaf ten  te  Amsterdam.     A  summary  of  the  work  relatfng ;  t "the pr 
of  metals  at  low  temperatures  will  be  found  in  articles  by  J. 

<6M- 8- 383 


390       PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

lated)  is  0.163,  while  at  4.185°  the  resistance  is  less  than  10~6,  and  at 
2.45°  less  than  2  X  10~10.  Similarly,  the  resistance  of  tin  vanishes  at  a 
temperature  of  3.78°  K.  and  that  of  thallium  at  2.3°  K.  The  resistance  of 
lead  vanishes  at  a  temperature  between  4.3°  and  20°,  probably  in  the 
neighborhood  of  6°  K.  Metals  in  a  condition  in  which  their  resistance 
vanishes  are  said  to  be  in  a  supraconducting  state.  Certain  metals,  such 
as  platinum  and  copper,  do  not  exhibit  supraconductance.  In  such 
metals  the  conductance  falls  to  a  low  limiting  value,  after  which  it 
remains  independent  of  temperature.  In  the  following  table  are  given 
values  for  the  resistance  of  platinum  in  arbitrary  units,  at  a  series  of 
temperatures. 

TABLE  CLV. 
RESISTANCE  OF  PLATINUM  AT  Low  TEMPERATURES. 

T  abs.  Resistance 

273.1  1.0 

20.1  0.0170 

14.3  0.0136 

4.3  0.0119 

2.3  0.0119 

1.5  0.0119 

It  is  apparent  from  this  table  that  at  a  temperature  in  the  neighborhood 
of  4.3°  absolute  the  resistance  of  platinum  falls  to  a  value  a  little  greater 
than  0.01  of  its  value  at  0°.  Below  this  temperature,  the  resistance 
remains  constant.  Similar  results  have  been  obtained  for  other  metals 
such  as  copper  and  iron.  Apparently,  those  metals,  which  exhibit  a 
marked  tendency  to  form  solid  solutions  with  other  metals,  do  not 
exhibit  the  phenomenon  of  supraconductance.  It  has  been  suggested 
that  the  absence  of  this  phenomenon  in  these  metals  is  due  to  the  influ- 
ence of  minute  traces  of  impurities. 

The  significance  of  the  phenomenon  of  supraconductance  is  not  fully 
understood  as  yet.  Various  theories  have  been  proposed  in  explanation 
of  this  phenomenon,  as,  for  example,  that  of  J.  J.  Thomson.9  Bridg- 
man 10  has  recently  suggested  that  a  polymorphic  change  takes  place  at 
the  point  where  supraconductance  intervenes.  According  to  this  view, 
the  normal  state  of  a  substance,  or  of  a  crystal,  at  very  low  temperatures 
is  that  of  supraconductance.  The  residual  resistance  found  in  the  case 
of  such  metals  as  platinum  is  due  to  non-homogeneity  between  the  sur- 
faces of  the  individual  crystals  of  which  the  conductor  is  composed.  At 

•J.  J.  Thomson,  Phil.  Mag.  SO,  192    (1915). 
10  Bridgman,  J.  Wash.  Acad.  11,  455. 


THE  PROPERTIES  OF  METALLIC  SUBSTANCES 


391 


the  present  time  it  is  not  possible  to  reach  any  certain  conclusion  as  to 
the  nature  of  these  phenomena. 

The  mean  temperature  coefficients  a  for  a  number  of  elementary  sub- 
stances are  given  in  Table  CLIII  above.     In  the  following  table  are 

1  dfy 
given  values  of  the  temperature  coefficient  a  =  —  -=-—  for  a  number  of 

tit    Ut 

metals  at  different  temperatures. 

TABLE    CLVI. 


TEMPERATURE  COEFFICIENT  ^  -5—  FOR  METALS  AT  DIFFERENT 

Rt  tit 


Temperature    Ag 

25°   0.0030 

100 0.0036 

200 0.0039- 

300 0.0040 

400 0.0042 

500 0.0044 

600 0.0046 

700 0.0047 

800  0.0052 

900  0.0058- 

1000 

1075  . 


TEMPERATURES. 

Fe 

Ni 

Al 

0.0052 

0.0043 

0.0034 

0.0068 

0.0043 

0.0040 

0.0090 

0.0070 

0.0042 

0.0111 

0.0080 

0.0043 

0.0133 

0.0036 

0.0046 

0.0147 

0.0030 

0.0050 

0.0170 

0.0028 

0.0060 

0.0224 

0.0026 

0.0120 

0.0120 

0.0025 

at  625° 

0.0046 

0.0028 

•  • 

0.0050 

0.0037 

f  . 

,  . 

0.0062 

.  . 

Mg 

0.0050 
0.0045 
0.0041 
0.0043 
0.0040 
0.0036 
0.0100 
0.0250 
at  625° 


Cu 

0.0036 
0.0038 
0.0040 
0.0041 
0.0042 
0.0043 
0.0044 
0.0047 
0.0053 
0.0057 
0.0062 


It  will  be  observed,  from  the  table,  that  the  temperature  coefficient  in- 
creases with  increasing  temperature.  The  magnitude  of  the  coefficients 
of  different  metals  differs  considerably,  particularly  those  of  the  magnetic 
metals,  iron  and  nickel.  It  is  interesting  to  note  that,  as  the  transition 
point  of  these  metals  is  approached,  the  temperature  coefficient  increases 
very  largely.  The  temperatures  at  which  the  transition  points  are 
reached  are  indicated  in  the  table  by  heavy  type.  Beyond  the  transition 
points,  the  temperature  coefficients  fall  back  to  normal  values,  in  the 
case  of  both  iron  and  nickel.  A  somewhat  similar  phenomenon  is  ob- 
served in  the  neighborhood  of  the  melting  point,  which  is  illustrated  in 
the  case  of  aluminium  and  magnesium,  particularly  in  the  case  of  the 
latter  element.  The  temperature  coefficient  increases  considerably  as  the 
melting  point  is  approached.  Beyond  the  melting  point,  the  coefficients 
are,  in  general,  smaller  than  below  this  temperature. 

The  temperature  coefficients  of  elementary  liquid  metals  vary  within 


392       PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

wide  limits.  The  coefficients  are  greatest  for  the  alkali  metals,  in  which 
case  they  differ  very  little  from  those  of  the  solids.  In  other  cases,  the 
temperature  coefficients  reach  extremely  small  values,  as,  for  example, 
in  that  of  zinc.  As  a  rule,  the  temperature  coefficients  of  liquid  metals 
have  values  in  the  neighborhood  of  one  fifth  that  of  the  solid  metals.  In 
the  following  table  are  given  the  mean  temperature  coefficients  of  a 
number  of  liquid  metals  referred  to  their  resistance  at  the  lowest  tem- 
perature given. 

TABLE   CLVII. 
TEMPERATURE  COEFFICIENT  OF  LIQUID  METALS. 

Temperature 
Metal  a  Interval 

Sodium   38.5    X  10"4                       M.P. 

Potassium  41.8    X  10~4                          " 

Lithium 27.3    X  10'4                     178-230 

Tin  5.9    X  10'4  M.P.-350 

Bismuth   4.1    X  10'4 

Thallium 3.5    X  10~4 

Cadmium  1.3    X  10-4 

Lead   5.2    X  10~4 

Copper 4.12  X  10'4  1084-1500 

Aluminium    5.42  X  HH  653-1250 

Iron   3.66  X10-4  1055-1650 

Nickel    1.67  X  1Q-4  1451-1650 

Zinc    0.3    XIO'4  419-500 

Tin 4.68  X  10'4  232-1600 

Cadmium 2.26  X  10~4                     500-650 

Antimony  1.37  X  10"4                     631-800 

The  temperature  coefficients  here  given  cannot  be  directly  compared 
with  those  of  the  solid  metals  at  ordinary  temperatures,  since  the  coeffi- 
cients are  referred  to  the  resistance  of  these  metals  at  higher  tempera- 
tures. In  a  number  of  instances  values  have  been  extrapolated  to  ordi- 
nary temperatures,  in  which  case  the  coefficients  are  invariably  smaller 
than  those  of  solid  metals.  For  example,  the  values  for  copper, 
aluminium  and  iron  are  7.45  X  10~4,  8.40  X  10'4  and  8.15  X  10'4,  re- 
spectively. 

The  temperature  coefficient  as  commonly  measured  is  the  resultant 
effect  of  temperature  change  and  volume  change.  The  temperature  coef- 
ficient at  constant  volume  differs  materially  from  that  at  constant  pres- 
sure, depending  upon  the  influence  of  pressure  upon  the  resistance  of  the 
conductor  in  question.  In  solid  metals,  the  pressure  effect  is  relatively 


THE  PROPERTIES  OF  METALLIC  SUBSTANCES  393 

small,  while  the  resistance-temperature  coefficient  is  large;  consequently, 
the  temperature  coefficient  is  not  greatly  affected  by  the  volume  change. 
In  liquid  metals,  however,  where  the  temperature  coefficient  is  small  and 
the  resistance  pressure  coefficient  relatively  large,  the  volume  change  has 
a  material  influence  on  the  observed  temperature  coefficient.  In  the  case  of 

mercury,11  the  resistance  temperature  coefficient  I  D  )  1  -JT  I   —  —  6.9  X 10'4 

as  against  the  value  of  +  8.9  X  10~4  for  the  resistance-temperature  coeffi- 
cient at  constant  pressure.  It  is  a  significant  fact  that  the  resistance  of 
a  liquid  metal  at  constant  volume  should  decrease  with  increasing  tem- 
perature. In  this  connection  it  may  be  noted  that  Somerville  12  -found 
that  zinc  wire,  wrapped  in  the  form  of  a  spiral  around  a  silica  tube, 
exhibited  a  marked  negative  temperature  coefficient  above  the  melting 
point,  the  resistance  varying  very  nearly  as  a  linear  function  of  the  tem- 
perature. In  this  case  the  metal  in  the  fluid  state  was  held  together  by 
surface  forces.  The  temperature  coefficient  of  molten  zinc  in  a  quartz 
tube  was  found  to  be  positive  but  of  a  very  low  value. 

5.  The  Conductance  of  Metallic  Alloys.  Metallic  alloys  may  be 
divided  into  four  classes  which  exhibit  distinct  properties.13  These  are: 
First,  solid  alloys  in  which  pure  crystals  of  the  constituent  elements  are 
present  in  intimate  contact;  second,  solid  alloys  in  which  mixed  crystals 
of  the  constituent  elements  are  present;  third,  solid  alloys  in  which  com- 
pounds of  the  constituent  elements  are  present;  and  fourth,  liquid  alloys. 
Among  the  solid  alloys,  several  of  these  types  often  appear  in  a  single 
alloy.  This  is  the  case,  for  example,  when  mixed  crystals  are  formed 
over  limited  concentration  intervals. 

a.  Heterogeneous  Alloys.    Except  in  so  far  as  the  resistance  of  alloys 
is  influenced  by  the  distribution  of  the  crystals  and  the  presence  of  resist- 
ance at  the  interface  between  crystal  elements,  solid  alloys  of  the  first 
class  do  not  differ  in  their  properties  from  pure  metals.    The  specific 
resistance  of  such"  alloys  is  a  linear  function  of  the  composition  and  with 
change  of  temperature  the  properties  vary  as  a  linear  function  of  the 
composition, 

b.  Homogeneous   Alloys.     Homogeneous   mixed    crystals    of   pure 
metallic  elements,  or  of  compounds,  form  an  important  class  of  substances 
which  are  remarkable  for  the  uniformity  of  their  behavior  among  them- 
selves and  the  divergence  of  their  behavior  from  that  of  their  constituent 
elements.    The  addition  of  a  second  metallic  component  to  another  metal, 

"Kraus,  Physical  Review  k,  159   (1914). 
12  Somerville,  Physical  Review  33,  77   (1911). 

u  A  summary  of  the  properties  of  metallic  alloys  is  given  by  Guertler,  Jahrb.  /.  Rad.  5, 
IT 


394       PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 


whether"  elementary  or  compound,  causes  a  marked  decrease  in  the  con- 
ductance of  the  resulting  homogeneous  alloy.  The  decrease  due  to  the 
addition  of  a  given  amount  of  the  second  constituent  is  the  greater  the 
lower  its  concentration.  If  the  conductance  is  represented  graphically 
as  a  function  of  the  composition  of  the  system,  the  resulting  curve  is 
throughout  convex  toward  the  axis  of  concentration.  The  minimum 
point  in  all  cases  lies  in  the  neighborhood  of  a  composition  of  50-50.  In 


o 

Au 


20        UO         60        SO 

Composition,  volume  per  cent. 


700 

Ag 


FIG.  68.    Representing  the  Conductance  of  Homogeneous  Alloys  of  Ag  and  Au  as  a 

Function  of  Composition. 

Figure  68  is  shown  the  conductance  curve  at  ordinary  temperatures  for 
homogeneous  mixtures  of  silver  and  gold.  As  may  be  seen,  the  conduct- 
ance of  either  component  is  greatly  reduced  on  the  addition  of  the  second 
constituent.  The  decrease  in  the  conductance  due  to  the  addition  of  a 
second  component  depends  upon  the  nature  of  the  substance  added  and  is, 
in  general,  the  greater  the  less  electropositive  the  added  constituent. 
Thus,  the  decrease  in  the  conductance  of  iron  due  to  the  addition  of 
carbon  or  silicon  is  much  greater  than  that  due  to  the  introduction  of 


THE  PROPERTIES  OF  METALLIC  SUBSTANCES 


395 


tungsten  or  nickel.  On  the  other  hand,  certain  variations  occur  in  the 
order  of  the  effects.  Thus,  due  to  the  addition  of  aluminium,  the  con- 
ductance of  iron  is  lowered  very  nearly  as  much  as  due  to  that  of  silicon. 
The  resistance-temperature  coefficient  of  solid  alloys  of  the  second 
class  likewise  varies  continuously  as  a  function  of  composition.  The 
curve  of  temperature  coefficients  is  similar  to  the  conductance  curve,  being 
convex  toward  the  axis  of  concentration  and  having  a  minimum  point  in 
the  neighborhood  of  a  composition  of  50-50.  In  Figure  69  is  shown  the 
curve  of  temperature  coefficients  for  alloys  of  silver  and  gold.  It  will 


0.004 


I    0*01 

a 

H  . 

"i 


90 


100 

A* 


Composition,  volume  per  cent. 
FIG.  69.    Temperature  Coefficient  of  Silver-Gold  Alloys  as  a  Function  of  Composition. 

be  observed  that  the  temperature  coefficient  falls  from  a  value  of  approxi- 
mately 4  X  10"3  for  the  pure  elements  to  7.5  X  10~4  for  an  alloy  contain- 
ing 50  volume  per  cent,  each,  of  the  constituents.  This  behavior  of  homo- 
geneous metallic  alloys  is  general.  In  many  cases,  the  effect  is  very 
pronounced  and  the  temperature  coefficient  falls  to  very  low  values. 

With  decreasing  temperature,  particularly  at  low  temperatures,  the 
resistance  of  homogeneous  metallic  alloys  decreases  nearly  as  a  linear 
function  of  the  temperature.  This  form  of  the  curve  persists  even  to  the 
lowest  temperatures  attainable.  Apparently,  then,  the  resistance  of 
alloys  of  this  type  approaches  a  finite  limiting  value  at  the  absolute  zero. 
In  the  following  table  are  given  values  of  the  resistance  of  manganin  wire 
(84  Cu,  12  Mn,  4  Ni)  down  to  liquid  helium  temperatures. 

TABLE  CLVIII. 
RESISTANCE  OF  MANGANIN  WIRE  AT  Low  TEMPERATURES. 


Temp  .....     16.5  —  193.1  —  201.7  —  253.3  —  258.0  —  269.0  —  271  5 
Resist  .....  124.20     119.35      117.90     113.42     112.91      111.92     111.71 


396       PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

Other  alloys  of  this  type  exhibit  a  similar  behavior  at  low  temperatures. 

At  high  temperatures,  the  resistance  curves  of  many  of  the  alloys  of 
this  type  are  very  -complex,  often  exhibiting  both  maxima  and  minima 
and  the  temperature  coefficient  at  times  becoming  negative.13*  The  curve 
for  manganin  wire,  for  example,  exhibits  two  maxima  at  approximately 
25°  and  475°  C.  and  two  minima  at  360°  and  525°  C.  respectively.  In  a 
few  instances,  the  temperature  coefficient  is  very  nearly  zero  over  a  large 
range  of  temperature,  as,  for  example,  in  the  case  of  advance  wire,  for 
which  the  temperature  coefficient  varies  very  little  up  to  a  temperature  of 
250°  C.  Taken  all  together,  the  resistance  curves  of  solid  solutions  of 
metals  are  very  complex  at  higher  temperatures. 

c.  Solid  Metallic  Compounds.  The  conductance  of  a  solid  compound 
of  two  elements  is  always  lower  than  that  of  one  of  the  constituents  and 
is  often  lower  than  that  of  both.  The  specific  resistance  of  a  compound 
relative  to  that  of  the  constituent  elements  depends  upon  the  nature  of 
the  elements  and  upon  tne  nature  of  the  compound  formed.  In  general, 
the  more  stable  the  compound,  the  higher  is  its  resistance  relative  to 
that  of  the  constituent  elements.  Compounds  between  strongly  electro- 
positive and  strongly  electronegative  metallic  elements,  as  a  rule,  exhibit 
a  very  high  specific  resistance.  In  the  following  table  are  given  values 
of  the  specific  conductance  of  a  number  of  compounds  at  room  tem- 
peratures. 

TABLE    CLIX. 
SPECIFIC  CONDUCTANCE  OF  A  NUMBER  OF  METALLIC  COMPOUNDS. 


Metal 

Mg2Sn 

Cu2Mg 

CuMg2 

MgZn2 

Mg3Bi2 

Al3Mn 

Al3Fe 

n  x  lo-4 

..  0.0912 

19.4 

8.38 

6.3 

0.76 

0.20 

0.71 

Metal 

Al3Ni 

AlMg 

Al2Mg3 

Al2Ag3 

AlAg3 

Sb2Te2 

TeSn 

H  X  10-4 

..  3.47 

2.63 

4.53 

3.85 

2.75 

0.48 

0.97 

Metal 

Bi2Te3 

SbAg3 

Cu3As 

MgAg 

Mg3Ag 

1*  X  10-* 

..  0.045 

0.93 

1.70 

20.52 

6.16 

It  will  be  observed,  from  the  table,  that  the  compound  between  mag- 
nesium and  tin  has  a  very  low  specific  conductance.  Where  two  ele- 
ments form  a  number  of  different  compounds,  that  compound,  in  gen- 
eral, has  the  lowest  specific  conductance  which  corresponds  to  the  normal 
electronegative  valence  of  the  less  metallic  element.  Thus,  the  specific 
conductance  of  Cu4Sn  is  much  lower  than  that  of  Cu3Sn  or  of  CuSn. 
The  low  value  of  the  specific  conductance  is  well  shown  in  the  case  of  the 
alloys  of  magnesium  and  tin  which  form  the  compound  Mg2Sn.  The 

»•  Somerville,  Phys.  Rev.  31,  261   (1910). 


THE  PROPERTIES  OF  METALLIC  SUBSTANCES  397 

specific  conductance  of  this  compound  at  25°  is  0.0912,  as  compared  with 
8.65  for  tin  and  22.73  for  magnesium. 

While  the  conductance  of  inter-metallic  compounds  is  thus,  in  gen- 
eral, very  low,  the  temperature  coefficient  of  these  compounds  is  of  the 
same  order  of  magnitude  as  that  of  pure  metals.  While,  therefore,  the 
addition  of  a  second  metallic  component  increases  the  resistance  of  the 
metallic  alloy,  whether  a  compound  or  a  solid  solution  is  formed,  so  that 
it  is  at  times  difficult  to  distinguish  between  these  two  cases  by  this 
means,  the  temperature  coefficient  of  the  resulting  alloy  will,  in  general, 
differ  widely  in  the  two  cases.  The  high  value  of  the  temperature  coeffi- 
cient of  metallic  compounds  and  the  low  value  of  this  coefficient  for 
homogeneous  alloys  afford  a  delicate  method  of  detecting  the  presence 
of  solid  solutions  in  metallic  alloys. 

d.  Liquid  Alloys.  The  properties  of  liquid  alloys  differ  greatly  from 
those  of  homogeneous  solid  alloys.  On  the  addition  of  a  second  com- 
ponent, the  conductance  of  a  liquid  metal  may  either  increase  or  de- 
crease. The  relative  conductance  of  the  two  substances  does  not  deter- 
mine the  magnitude  and  sign  of  the  initial  conductance  change.  If  the 
specific  conductance  of  two  metals  is  nearly  the  same,  the  conductance 
curves  often  exhibit  maxima  or  minima  and  sometimes  both  maxima  and 
minima.  In  Figure  70  are  shown  the  conductance  curves  for  mixtures 
of  mercury  with  bismuth,  lead,  tin  and  cadmium.  Small  additions  of 
these  elements  to  mercury  cause  a  relatively  large  initial  rise  of  the 
conductance  curve.  This  rise  is  particularly  noteworthy  in  the  case  of 
bismuth,  which  itself  is  a  relatively  poor  conductor.  The  four  curves  are 
evidently  similar.  With  bismuth  and  lead,  whose  specific  conductances 
are  relatively  low,  both  a  maximum  and  a  minimum  occur  in  the  con- 
ductance curve.  With  tin  the  maximum  and  minimum  have  disappeared, 
but  an  inflection  point  is  present  in  the  conductance  curve.  The  curve 
for  alloys  of  cadmium  and  mercury  exhibits  a  constant  curvature.  The 
four  elements,  the  conductance  of  whose  amalgams  are  shown  in  the 
figure,  do  not  form  compounds  with  mercury  according  to  their  melting 
point  diagrams. 

The  behavior  of  amalgams,  in  which  compounds  are  formed,  differs 
markedly  from  that  of  amalgams  in  which  compounds  are  absent.  The 
addition  of  small  amounts  of  lithium,  calcium  and  strontium  increases 
the  conductance  of  mercury,  while  that  of  potassium,  sodium,  caesium 
and  barium  reduces  its  conductance.14  With  increasing  temperature,  the 
relative  effect  of  such  addition  is  increased.  According  to  Hine,15  the 

14  H.  Fenninger,  Dissertation,  Freiberg,  1914 ;  J.  Koenigsberger,  loc.  cit.t  p.  654. 
»»Hine,  J.  Am.  Chem.  Soc.  39,  890  (1917). 


398        PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

specific  conductance  of  sodium  amalgams  passes  through  a  minimum  at 
about  2.5  atom  per  cent  of  sodium.  McCoy  and  West 15a  have  determined 
the  conductance  of  amalgams  of  substituted  ammonium  bases.  The 
conductance  of  these  amalgams  decreases  with  increasing  concentration, 
passing  through  a  minimum.  In  general,  liquid  alloys  whose  components 
do  not  form  compounds  exhibit  conductance  curves  without  pronounced 
minima.  On  the  other  hand,  alloys  which  form  compounds  often  exhibit 
pronounced  minima.  This  is,  for  example,  the  case  with  alloys  of  sodium 
and  potassium.  In  the  following  table  are  given  conductance  values  of 
mixtures  of  sodium  and  potassium,  together  with  their  temperature  coeffi- 
cients.18 

TABLE    CLX. 

CONDUCTANCE  OF  LIQUID  SODIUM-POTASSIUM  ALLOYS  AT  200°. 

Specific 
Atom  Per  Cent  Conductance 

Potassium  \i  X  10~4  a  X  103 

0  7.37  +3.85 

4.2  5.55  3.222 

8.0  4.42  2.43 

26.5  2.690  1.725 

44.5  2.150  1.555 

63.0  5.095  1.585 

82.0  2.250  1.860 

93.0  3.230  2.91 

100.0  4.59  4.98 

It  will  be  observed  that  the  conductance  curve  exhibits  a  minimum  in 
the  neighborhood  of  50  atomic  per  cent  of  sodium  and  potassium,  which 
corresponds  with  the  composition  of  the  compound  NaK.  The  existence 
of  this  compound  has  been  established  by  means  of  the  melting  point 
diagram.  It  will  be  observed,  also,  that  the  temperature  coefficient  of  the 
sodium-potassium  alloys  exhibits  a  minimum  value  at  a  composition  cor- 
responding with  that  of  the  compound.  The  conductance  of  alloys  of 
copper  and  lead  exhibits  neither  a  maximum  nor  a  minimum,  but  the  tem- 
perature coefficient  exhibits  a  minimum  at  a  composition  in  the  neighbor- 
hood of  40  per  cent  of  lead.  The  conductance  curves  of  liquid  alloys  of 
copper  and  antimony  exhibit  singularities  corresponding  with  the  com- 
position of  the  compounds  Cu4Sb  and  Cu3Sb.  The  temperature  coeffi- 
cients of  both  these  compounds  are  negative,  while,  those  of  the  pure 
metals  are  positive.  The  conductance  curve  for  liquid  mixtures  of  copper 

»«  McCoy  and  West,  J.  Phys.  Chem.  16,  261   (1912), 
16  Koenigsberger,  \oc.  cit, 


THE  PROPERTIES  OF  METALLIC  SUBSTANCES 


399 


and  tin  likewise  exhibits  singularities,  which  indicate  the  formation  of 
compounds.  The  temperature  coefficients  of  these  compounds  are 
negative. 

It  may  be  concluded  that  liquid  alloys,  in  which  compounds  are 
formed,  exhibit  properties  which  differ  markedly  from  those  of  alloys  in 
which  compounds  are  not  formed.  When  the  compounds  formed  are 
very  stable,  the  conductance  of  the  resulting  alloy  is  usually  less  than 
that  of  the  pure  components.  The  temperature  coefficient  of  fused  metal- 
lic compounds  is,  as  a  rule,  either  very  small  or  negative. 


0 

Hg 


?0    2O    JO 


£0    6O    70    80    90    700 

B 

Weight  Per  Cent  B 

FIG.  70.     Conductance  of  Liquid  Amalgams  as  a  Function  of  Composition. 


6.  Variable  Conductors.  Within  this  class  are  included  those  ele- 
mentary substances  which  lie  upon  the  border  line  between  metallic  and 
nonmetallic  elements.  There  are  also  included  a  considerable  number 
of  metallic  compounds  in  which  one  of  the  constituents  is  strongly  electro- 
negative. The  elementary  substances  comprised  within  this  class  often 
appear  both  in  a  metallic  and  in  a  nonmetallic  state.  Carbon  is  a  typi- 
cal example  of  this  type  which,  in  the  form  of  diamond,  is  a  noncon- 
ductor, and,  in  the  form  of  graphite,  a  relatively  good  conductor.  Many 
of  the  metallic  compounds,  also,  may  appear  both  in  a  conducting  and  in 
a  nonconducting  state,  as,  for  example,  various  sulphides  and  oxides 


400        PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

which  are  metallic  in  a  crystalline  state  and  which   are  nonmetallic 
when  precipitated  from  solution. 

The  specific  conductance  of  the  metals  of  this  class  is  often  relatively 
low.  In  the  following  table  are  given  values  of  the  specific  conductance 
of  a  few  of  these  metals. 

TABLE    CLXI. 
SPECIFIC  CONDUCTANCE  OF  VARIOUS  SUBSTANCES  AT  0°. 

Conductor  Specific  Conductance 

Graphite  (Siberia)    ...................  8.71  X  102 

Silicon  (+  3.3%  impur.)  ........  .  ......  10.0 

Titanium  ............................  2.8  X  103 

Zirconium    ...........................  5     X  103 

CuS   .  ...............................  8.5  X103 

Pb02   ...............................  4.3  X  103 

CdO  ................................  8.3  X  102 

PbS    ................................  4.2  X  102 

Fe304   ...............................  1.16  X102 

FeS2   (Pyrite)    .......................  0.42  X  102 

FeS2   (Marcasite)    ...  .................  0.06 

The  resistance  of  metals  of  this  class  at  lower  temperatures  decreases 
greatly  with  increasing  temperature,  approximately  as  an  exponential 
function.  At  higher  temperatures,  the  conductance  reaches  a  minimum 
value,  after  which  it  increases  approximately  as  a  linear  function  of  the 
temperature.  A  familiar  example  of  this  type  of  substance  is  carbon. 
It  is  uncertain,  however,  that  the  observed  conductance  curves  of  this 
type  actually  relate  to  pure  substances.  Kammerlingh  Onnes  and  Hof  17 
have  shown,  for  example,  that  graphite  may  be  purified  to  a  point  where 
its  resistance  decreases  with  temperature  down  to  approximately  —  173° 
with  a  coefficient  of  0.0029.  At  lower  temperatures  the  resistance  de- 
creases somewhat  more  rapidly.  Similar  results  have  been  obtained  in 
the  case  of  bismuth.  In  the  earlier  experiments  of  Dewar  and  Fleming/8 
bismuth  was  found  to  exhibit  a  minimum  resistance  at  temperatures 
varying  from  room  temperatures  to  —  80°  C.,  depending  upon  the  purity 
of  the  sample.  Later,  however,  this  element  was  purified  to  a  point  where 
its  resistance  decreased  throughout  with  decreasing  temperature  down  to 
liquid  hydrogen  temperatures.19  Since  many  of  the  substances  of  this 
class  cannot  be  prepared  readily  in  a  pure  state,  it  follows  that  the  pecu- 


17  K.  Onnes  and  Hof,  KoninkUjke  Akad,  van  Wetensch.  Amsterdam  11,  520   (1914). 
"Dewar  and  Fleming,  Phil.  Mag.  W,  303   (1895). 

18  J.  Clay,  Dissertation,  Leiden   (1908)  ;  Jahrb.  f.  Rad.  8,  391   (1911). 


THE  PROPERTIES  OF  METALLIC  SUBSTANCES  401 

liar  form  of  the  conductance  curve  may  be  due  primarily  to  the  presence 
of  impurities. 

Many  of  these  substances  exhibit  transition  points  at  which  the  resist- 
ance changes  discontinuously.  In  some  instances  these  processes  are 
reversible  and  in  others  irreversible.  Silicon  exhibits  transition  points 
at  approximately  220°  and  440°.  Titanium  exhibits  discontinuities  in 
the  neighborhood  of  300°  and  600°,  the  first  of  which  is  slowly  reversible 
and  the  second  irreversible. 

Among  variable  conductors  are  included  many  compounds  on  the 
borderline  between  metallic  and  nonmetallic  substances.  These  com- 
pounds often  appear  in  several  modifications  whose  properties  may  differ 
greatly.  For  example,  silver  sulphide,  which  has  already  been  mentioned 
in  a  preceding  chapter,  conducts  electrolytically  in  one  form,  while  in 
another  form  it  exhibits  mixed  electrolytic  and  metallic  conduction. 
Many  solid  oxides  and  mixtures  of  oxides,  which  at  ordinary  temper- 
atures are  nonmetallic,  appear  to  conduct  the  current  metallically  at 
high  temperatures.  The  Nernst  filament  is  a  familiar  example  of  this 
type  of  conductor.  While  it  is  possible  that  a  portion  of  the  current  in 
some  of  these  substances  is  carried  electrolytically,  the  greater  portion 
appears  to  be  carried  metallically. 

As  the  compounds  become  more  distinctively  metallic,  which  is  as  a 
rule  the  case  as  the  more  electronegative  element  becomes  more  metallic 
and  the  more  electropositive  element  becomes  less  metallic,  the  conduct- 
ance approaches  that  of  typical  metallic  compounds.  In  such  cases,  the 
temperature  coefficient  becomes  less  negative  or  even  positive.  In  gen- 
eral, the  higher  the  conductance  of  a  compound,  the  greater  is  the  value 
of  its  positive  temperature  coefficient. 

Many  of  the  conductors  belonging  to  this  class  exhibit  singular  prop- 
erties. In  many  cases,  also,  systems,  which  might  not  be  expected  to 
exhibit  metallic  properties,  nevertheless  belong  to  this  class  of  conductors. 
Such  is,  for  example,  the  case  with  cuprous  iodide,  Cul,  which  absorbs 
iodine  reversibly.  The  resulting  product  conducts  the  current  metal- 
lically and  its  conductance  is  the  greater  the  greater  the  amount  of  iodine 
absorbed.  The  smaller  the  resistance  of  the  iodide,  the  greater  is  the 
value  of  the  positive  temperature  coefficient.  As  the  specific  resistance 
increases,  the  temperature  coefficient  becomes  negative. 

The  examples  of  this  class  of  substance  are  extremely  numerous  and 
a  great  deal  of  experimental  material  is  available.  It  is  not  to  be  doubted 
that  a  study  of  such  systems  will  throw  a  great  deal  of  light  on  the  nature 
of  the  conduction  process  and  conceivably  on  the  constitution  of  metallic 


402        PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

compounds.  A  more  detailed  discussion,  however,  is  not  possible  in  this 
monograph.20 

7.  The   Conductance    of   Metals   as   Affected    by    Other   Factors. 
a.    Anisotropic  Metallic  Conductors.    As  might  be  expected,  the  con- 
ductance of  many  crystalline  substances  depends  upon  the  orientation  of 
the  crystal.    Thus,  the  conductance  of  a  crystal  of  bismuth  at  right 
angles  to  its  base  at  15°  is  1.78  times  that  parallel  to  its  base.21    It  has 
been  shown  that  the  conductance  of  a  bismuth  crystal  may  be  represented 

.  by  means  of  an  ellipsoid  of  rotation.22 

b.  Influence  of  Mechanical  and  Thermal  Treatment.    The  conduct- 
ance of  metals  is  dependent  upon  their  previous  mechanical  and  thermal 
treatment.    Wires  which  are  hard  drawn  in  general  exhibit  a  lower  con- 
ductance than  do  annealed  wires.    The  thermal  treatment  of  metals  has 
an  influence  on  their  conductance,  not  only  in  that  it  tends  to  relieve 
mechanical  stresses  resulting  from  previous  mechanical  treatment,  but 
also  in  that  it  tends  to  induce  various  transformations  in  the  body  of  the 
metal,  some  of  which  are  reversible  and  others  of  which  are  irreversible. 

c.  The  Influence  of  Pressure  on  Conductance.    The  resistance  of 
most  metallic  elements  is  decreased  under  the  action  of  uniform  pressure. 

The  coefficient  -~  -3-  for  solid  metallic  elements  varies  between— 15.1  XlO'7 
R  dp 

for  nickel  and  — 152  X  10~7  for  lead.  For  bismuth  the  value  of  the 
coefficient  is  positive  and  equal  to  +  196  X  10~7.  The  resistance  does 
not  vary  as  a  linear  function  of  the  pressure,  the  pressure  coefficient  de- 
creasing with  increasing  pressure.  The  resistance  of  manganin  wire 
varies  very  nearly  as  a  linear  function  of  the  pressure.  The  only  pure 
liquid  metal  for  which  data  are  available  is  mercury.  At  25°,  the  value 
of  its  resistance-pressure  coefficient  is  —  334  X  10~7.  It  would  be  inter- 
esting to  know  whether  other  liquid  metals  exhibit  a  similarly  high  value 
of  this  coefficient. 

The  influence  of  pressure  on  the  resistance  of  variable  conductors  is 
often  extremely  marked.23 

d.  Photo-electric  Properties.    A  few  substances  are  sensitive  to  the 
action  of  light.    Selenium  is  the  most  remarkable  example  of  this  type 
of  substances.    The  influence  of  light  and  various  other  factors  on  the 
conductance  of  selenium  has  occupied  the  attention  of  a  great  many  inves- 
tigators.   A  detailed  discussion  cannot  be  given  here.24 

8.  Relation  between  Thermal  and  Electrical  Conductance  in  Metals. 

80  A  very  complete  summary  is  given  by  Koenigsberger,  loc.  cit.,  pp.  661-680. 
"Lownds,  Ann.  d.  Phys.  9,  681   (1902). 

22  van  Everdingen,  Versl.  Akad.  van  Wetensch.  Amsterdam  3,  316  and  407  (1900), 

23  For  references,  see  Koenigsberger,  loc.  cit.,  pp.  694-7. 
*«  For  references,  see  Koenigsberger,  Iqc.  cit.,  pp.  681-694, 


THE  PROPERTIES  OF  METALLIC  SUBSTANCES  403 

As  was  first  pointed  out  by  Wiedemann  and  Franz,25  the  thermal  con- 
ductance of  metals  at  ordinary  temperatures  is  very  nearly  proportional 
to  their  electrical  conductance.  Subsequent  investigations 26  have  shown 
that  the  ratio  of  thermal  to  electrical  conductance  is  not  a  constant,  but 
increases  with  increasing  temperature.  Lorenz  2T  showed  that  the  ratio 

of  thermal  to  electrical  conductance  -  for  pure  metallic  substances  and 

H 

some  alloys  increases  approximately  as  a  linear  function  of  the  absolute 
temperature,  the  coefficient  being  very  nearly  equal  to  the  coefficient  of 
expansion  of  gases.  Since  the  resistance  varies  approximately  as  a  linear 
function  of  the  absolute  temperature,  it  follows  that  the  thermal  con- 
ductance of  metals  is  relatively  independent  of  temperature.  At  very  low 
temperatures,  however,  the  thermal  conductance  of  metals  increases 
markedly.  Nevertheless,  as  K.  Onnes  and  Hoist,28  have  shown,  the 
thermal  resistance  of  metals  does  not  approach  a  value  of  zero  in 
regions  where  metals  are  in  the  supraconducting  state.  For  example,  at 
its  melting  point,  the  thermal  conductance  of  mercury  is  0.075;  between 
4.5°  K  and  5.1°  K  it  is  0.27;  and  between  3.7°  K  and  3.9°  K  it  is  0.40. 
At  very  low  temperatures,  therefore,  the  thermal  and  electrical  conduct- 
ance do  not  follow  a  parallel  course. 

The  thermal  conductance  of  alloys  varies  with  composition  in  a  man- 
ner somewhat  similar  to  that  of  the  electrical  conductance.  The  change 
in  thermal  conductance,  due  to  a  given  change  in  composition,  is  consid- 
erably smaller  than  is  the  corresponding  change  in  electrical  conduct- 
ance. The  thermal  conductance  curves  of  alloys  which  form  a  complete 
series  of  mixed  crystals  exhibit  a  minimum  similar  to  that  of  the  elec- 
trical conductance  curves.  The  relative  decrease  of  the  thermal  con- 
ductance, however,  is  much  smaller  than  that  of  the  electrical  conduct- 
ance. Accordingly,  the  ratio  of  the  thermal  to  the  electrical  conductance 
for  homogeneous  alloys  is  considerably  greater  than  it  is  for  pure  metals. 
Somewhat  similar  relations  are  found  in  the  case  of  metallic  compounds. 
While  compounds  in  general  exhibit  a  lower  thermal  conductance  than 
do  the  pure  components,  the  ratio  of  thermal  to  electrical  conductance  is 
larger  for  the  compounds  than  it  is  for  pure  metals. 

The  thermal  conductance  of  variable  conductors  is  often  as  great  as 
that  of  typical  metallic  elements.  Since  the  electrical  conductance  of 

these  substances  is  relatively  low,  the  ratio  —  for  these  substances  is  often 

"Wiedemann  and  Franz,   Pogg.  Ann.  89,  497   (1853)  ;  ibid.,  95,  338   (1895). 
26 The  literature   relating  to   this  subject  has   been   collected   in   various   handbooks; 
see  footnote,  p.  385. 

27  L.  Lorenz,  Pogg.  Ann.  U{1,  429   (1872)  ;  Wied.  Ann.  IS,  422   (1881). 
»K.  Onnes  and  Hoist,  Proc.  Amsterdam   Acvd.  171,  760   (1914). 


404       PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

very  great.    Thus  the  value  of  -   for  graphite,  silicon  and  hematite 

(Fe203)  is  2.5  X  1012,  6.8  X  1014  and  7.3  X  1014  respectively.  For  ordi- 
nary metals  the  value  is  in  the  neighborhood  of  6.7  X  1010  at  room  tem- 
peratures.29 In  this  connection  it  is  interesting  to  note  that  the  thermal 
conductance  of  some  nonmetallic  crystals  is  greater  than  that  of  many 
metallic  substances.  Thus,  the  thermal  conductance  of  rock  salt  is 
0.0137  and  that  of  quartz  -L  to  its  axis  is  0.0263,  while  that  of  bismuth  is 
0.0194.  While  thermal  and  electrical  conductance  are  intimately  related, 
the  fact  that  some  nonmetals  are  likewise  excellent  thermal  conductors 
should  not  be  lost  sight  of. 

9.  Thermoelectric  Phenomena  in  Metals.  We  have  to  consider  three 
related  thermoelectric  phenomena,  namely:  1,  the  electromotive  force 
arising  in  a  metallic  system  as  a  result  of  a  temperature  difference  be- 
tween the  junctions  of  two  metals;  2,  the  Peltier  effect  which  is  a  heat 
transfer  taking  place  when  a  current  passes  through  a  junction  between 
two  different  metallic  conductors;  and,  3,  the  Thomson  effect  which  is  a 
heat  transfer  accompanying  the  passage  of  the  current  through  a  con- 
ductor in  which  a  temperature  gradient  exists.  From  a  practical  point 
of  view,  the  first  of  these  effects  is  the  most  important  and  has  been 
investigated  most  extensively. 

The  thermoelectric  force  of  a  thermocouple  may  be  expressed  very 
nearly  as  a  function  of  the  temperature  by  means  of  an  equation  of  the 
form: 


Usually  a  quadratic  equation  suffices.  For  smaller  temperature  differ- 
ences, the  sign  of  the  constant  a  corresponds  with  the  direction  of  the 
thermoelectric  force.  The  sign  of  this  electromotive  force  depends  upon 
the  nature  of  the  metals.  Let  us  call  the  effect  positive  for  the  two  metals 
AB,  when  the  current  flows  from  A  to  B  at  the  cold  junction.  The  metal 
A  will  then  be  said  to  be  positive  with  respect  to  B.  The  values  of  the 
coefficients  a  and  |3  for  different  metals  with  respect  to  lead,  the  cold 
junction  being  kept  at  a  temperature  of  0°  C.,  are  given  in  Table  CLXII. 
As  may  be  seen  from  the  table,  metals  which  are  closely  related  often 
have  thermoelectric  constants  which  are  opposite  in  sign;  thus,  lithium 
and  potassium  stand  in  reverse  order  to  lead,  which,  in  the  table,  is  taken 
as  a  standard.  So,  also,  the  closely  related  elements,  antimony  and 
bismuth,  which  exhibit  a  relatively  high  thermoelectric  power,  lie  near 

n  See  Koenigsberger,  IQC.  eft.,  p.  720-, 


THE  PROPERTIES  OF  METALLIC  SUBSTANCES  405 

TABLE   CLXII. 

VALUES  OF  THE  THERMOELECTRIC  COEFFICIENTS  a  AND  (3  WITH  RESPECT 
TO  LEAD  IN  MICROVOLTS  PER  DEGREE. 

Metal  Si          Tea       Sb  ||         Fe  Li  Ag  Pb 

a +443      + 163    +  22.6     +  13.4     + 11.6      +  2.3  0 

(3  X  102    . .          . .  . .  . .        —  3.0      +3.9       -f-  0.76 

Metal  Mg  Sn         Na  K  Co          Ni          Bi  || 

a —0.12    —0.17    —4.4    —11.6—20.4    —23.3    —127.4 

(3  X  102    . .   4-  0.20     +  0.20      -  2.1      —  2.5        -  7.5      —  0.8      —  70. 

the  opposite  ends  of  the  table.  Similar  inversions  are  found  in  the  case 
of  other  closely  related  elements,  such  as  iron,  cobalt  and  nickel. 

In  alloys,  the  thermoelectric  force  is,  in  general,  a  function  of  the 
composition.  The  thermoelectric  force  of  heterogeneous  alloys  varies 
approximately  as  a  linear  function  of  the  composition,  while  that  of 
homogeneous  alloys,  in  general,  exhibits  a  marked  minimum  somewhat 
similar  to  that  of  the  conductance  curve.  The  thermoelectric  power  of  a 
compound,  in  general,  differs  from  that  of  its  component  elements.  The 
formation  of  compounds  by  a  given  pair  of  elements  is  indicated  by  dis- 
continuities in  the  curves  connecting  the  thermoelectric  force  with  the 
mean  composition  of  the  alloy.  As  a  rule,  the  thermoelectric  force  is 
high  for  compounds  which  are  relatively  poor  conductors.  For  a  more 
detailed  discussion  of  the  thermoelectric  properties  of  metals  the  reader 
is  referred  to  the  various  handbooks  in  which  these  data  have  been 
collected. 

10.  Galvanomagnetic  and  Thermomagnetic  Properties.  When  a  cur- 
rent of  electricity  flows  through  a  conductor,  the  distribution  of  the 
current  in  the  conductor  is  altered  under  the  action  of  an  external  mag- 
netic field.  The  effects  observed  depend  upon  the  relative  direction  of 
the  current  and  of  the  field.  The  application  of  the  magnetic  field,  there- 
fore, gives  rise  to  potential  differences  between  points  in  the  conductor 
which  normally  are  at  the  same  potential.  With  a  field  acting  at  right 
angles  to  the  direction  of  the  current  flow,  potential  differences  arise  in 
the  conductor  transverse  to  the  magnetic  field,  one  at  right  angles  to  the 
direction  of  the  current  flow  and  the  other  parallel  to  this  direction. 
With  a  longitudinal  field,  that  is,  a  field  acting  parallel  to  the  direction 
of  the  current  flow,  only  a  single  effect  is  observable;  namely,  an  electro- 
motive force  parallel  to  the  direction  of  current  flow.  Similar  effects 
are  observed  when  a  current  of  heat  flows  through  a  conductor  in  a  mag- 


406       PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

netic  field.  Conversely,  when  a  current  flows  through  a  conductor  in  a 
magnetic  field,  temperature  differences,  as  well  as  potential  differences, 
arise  in  the  conductor.  Altogether,  there  are  twelve  effects  of  this  type: 
four  thermomagnetic  effects  in  transverse  fields,  two  thermomagnetic 
effects  in  longitudinal  fields,  four  galvanomagnetic  effects  in  transverse 
fields,  and  two  galvanomagnetic  effects  in  longitudinal  fields. 

Of  these  various  effects,  the  transverse  galvanomagnetic  effect  in  a 
transverse  field  has  been  studied  most  extensively.  This  is  commonly 
known  as  the  Hall  effect.  The  relation  between  the  electromotive  force 
and  the  variables  of  the  system  are  given  by  the  equation: 

_  RHi 
D   ' 

where  H  is  the  field  intensity,  i  is  the  total  current  flowing,  and  D  is  the 
thickness  of  the  conducting  sheet  carrying  the  total  current  i.  R,  which 
is  the  constant  of  the  Hall  effect,  is  a  property  of  the  conductor  in  ques- 
tion. This  constant  varies  greatly  for  different  metals  and  may  have 
either  positive  or  negative  values.  As  a  rule,  the  effect  is  greatest  in 
substances  of  relatively  low  conducting  power.  It  is  particularly  marked 
in  bismuth.  Here,  however,  as  might  be  expected,  the  value  of  the  coeffi- 
cient depends  upon  the  orientation  of  the  crystal.  Since  the  flow  of 
current  in  a  conductor  is  influenced  by  an  external  magnetic  field,  it  fol- 
lows that  the  resistance  of  a  conductor  will  be  influenced  by  an  external 
field. 

At  low  temperatures,  the  influence  of  a  magnetic  field  on  the  resist- 
ance becomes  marked,  particularly  for  bismuth.  K.  Onnes  30  has  shown 
that  at  very  low  temperatures,  where  metals  are  normally  in  the  supra- 
conducting  state,  the  curves  connecting  resistance  and  field  strength  are 
similar  to  those  connecting  resistance  and  temperature.  The  action  of 
transverse  and  longitudinal  fields  differs  little.  For  lead  and  tin  the 
critical  value  of  the  field  strength  at  which  the  resistance  rises  abruptly 
to  measurable  values  lies  between  500  and  700  G.  It  varies  slightly  with 
temperature. 

The  various  galvanomagnetic  and  thermomagnetic  effects  would  ap- 
pear to  be  of  great  importance  from  a  theoretical  standpoint;  for,  if  a 
current  is  carried  by  charged  particles,  the  observed  effects  must  be  due 
to  the  reaction  of  the  field  on  these  particles.  It  might  be  expected  that 
the  reaction  of  the  field  on  the  moving  particles  in  a  metallic  conductor 
would  be  similar  to  that  observed  in  the  case  of  the  cathode  rays.  Actu- 
ally, however,  the  observed  effect  in  the  case  of  most  metallic  conductors 

•°Ver8l.  Akadf  van  Wetensch.  Amsterdam  23,  493  (1914).     See  also  J.  Clay,  Joe.  cit. 


THE  PROPERTIES  OF  METALLIC  SUBSTANCES  407 

is  in  a  direction  opposite  to  that  observed  in  the  case  of  P  particles,  assum- 
ing that  the  conducting  particles  in  metals  are  negatively  charged.  Since 
a  great  many  facts  indicate  that  the  current  in  metallic  conductors  is  not 
carried  by  positive  particles,  it  appears  that  the  various  galvanomagnetic 
effects  cannot  be  accounted  for  by  a  simple  theory  of  this  type.  A  num- 
ber of  theories,  that  of  J.  J.  Thomson  for  example,  have  been  suggested 
to  account  for  the  Hall  effect  and  similar  phenomena.81  At  the  present 
time,  however,  a  satisfactory  theory  of  these  effects  does  not  exist.  In- 
deed, the  same  may  be  said  of  the  theory  of  the  conduction  process  in 
metals  under  normal  conditions.  It  may  be  expected,  however,  that 
ultimately  the  thermomagnetic  and  galvanomagnetic  effects  will  play  an 
important  role  in  the  development  of  the  theory  of  metallic  conduction. 

A  detailed  study  of  the  properties  of  conductors  in  a  magnetic  field 
would  lead  far  beyond  the  scope  of  the  present  monograph.  The  ob- 
served facts  will  be  found  summarized  in  the  references  already  given. 

11.  Optical  Properties  of  Metals.    According  to  the  electromagnetic 
theory,  the  electrical  and  optical  properties  of  metallic  substances  are 
intimately  related.    The  reflecting  power  and  absorbing  power  of  metals, 
according  to  this  theory,  should  be  very  great.    From  the  known  values 
of  the  conductance  of  metallic  substances,  the  optical  constants  of  these 
substances  may  be  derived  for  long  wave  lengths  when  selective  action 
does  not  occur. 

The  theory  of  the  optical  effects  in  metals,  together  with  the  most 
important  facts,  will  be  found  summarized  in  treatises  on  electricity  and 
magnetism  and  on  physical  optics.32 

12.  Theories  Relating  to  Metallic  Conduction.    The  theory  of  metal- 
lic conduction,  like  the  theory  of  electrolytic  conduction,  is  still  in  a  very 
unsatisfactory  state.    Qualitatively,  the  theory  that  the  current  is  carried 
by  negative  electrons  is  in  good  agreement  with  the  facts,  but  a  satisfac- 
tory quantitative  theory  has  not,  as  yet,  been  established.    The  difficulties 
confronting  a  comprehensive  theory  of  metallic  conduction  are,  indeed, 
very  great,  as  is  apparent  when  it  is  considered  how  many  detailed  facts 
must  be  accounted  for.    A  number  of  theories  which  have  been  proposed 
are  able  to  account  for  a  limited  number  of  the  properties  of  metals  in  a 
fairly  satisfactory  manner.    So,  for  example,  the  theories  of  Drude  and 
of  Thomson  render  an  account  of  the  relation  between  the  thermal  and 
the  electrical  conductance  of  metals  and,  to  some  extent,  also,  of  the 
thermo-  and  galvanomagnetic  effects  and  thermoelectric  effects  in  metals. 
On  the  whole,  however,  these  theories  are  far  from  satisfactory.    They 

"  J.  J.  Thomson,  Rapp.  Congr.  Phys.  3,  143,  Paris  (1900). 

"  See,    for   example,    VVinkelmaun,    Handbuch   d.   Physik ;   Oraetz     Handbuch   d 
trizitat  u.  d.  Magnetismus,  etc. 


408       PROPERTIES  OF  ELECTRICALLY  CONDUCTING  SYSTEMS 

are  not  able  to  account  for  the  properties  of  metallic  substances  at  very 
low  temperatures.  Neither  are  they  able  to  account  successfully  for 
the  properties  of  alloys  and  of  liquid  metals.33 

It  is  obvious  that  the  electrical  properties  of  metallic  substances  are 
extremely  sensitive  to  all  agencies.  Temperature  and  density,  as  well  as 
all  external  forces,  have  a  marked  influence  upon  the  electrical  properties 
of  metals,  and  particularly  on  the  conductance.  So,  also,  the  properties 
of  metallic  substances  are  very  sensitive  to  change  in  the  state  of  the 
system.  The  formation  of  compounds,  of  mixed  crystals,  or  any  poly- 
morphic change  is  invariably  accompanied  by  a  great  change  in  electrical 
properties.  Ultimately,  it  would  appear  that  a  study  of  the  electrical 
properties  of  metals,  and  particularly  of  metallic  compounds,  should  yield 
some  clue  as  to  the  constitution  of  these  substances.  At  the  present  time, 
however,  the  constitution  of  metallic  substances,  and  particularly  of 
metallic  compounds,  remains  an  unsolved  problem. 

18  Very  complete  references  to  the  theories  dealing  with  metallic  conduction  are  given 
by  Koenigsberger,  loc.  cit.,  p.  385,  above. 


SUBJECT  INDEX 


Acetone,  conductance  of  CoCl2  in — at  dif- 
ferent temperatures,  163 ;  —  conductance 
of  Nal  in,  47  ;  —  values  of  A0  in,  62  ;  — 
values  of  mass-action  constant  in,  62 

Acid,  acetic,  mass-action  constant  of,  43 ; 
—  amides,  nature  of,  315  ;  —  formic,  hy- 
drolytic  equilibria  in,  230 ;  —  formic, 
solution  of  formates  in,  101 ;  —  sulphuric, 
intermediate  ions  in  aqueous  solutions  of, 
148  ;  —  trichlorobutyric,  mass-action  con- 
stant of,  44 

Acids,  conductance  of — in  alcohol-water 
mixtures,  181 

Activity  Coefficient  of  T1C1  from  solubility 
data,  337 ;  —  Coefficient,  definition  of, 
331 ;  —  Coefficient,  numerical  values  for 
concentrated  solutions,  334 ;  —  Coeffi- 
cient, numerical  values  for  dilute  solu- 
tions, 333 ;  —  Coefficient,  values  obtained 
by  different  methods  compared,  334 ;  — 
definition  of,  331 

Alcohol,  ethyl,  conductance  of  Nal  in,  47  ; 
— -  ethyl,  solubility  of  phenylthiourea  in — 
in  presence  of  electrolytes,  250 

Alcohols,  influence  of  water  on  conduct- 
ance of  acids  in,  181 

Alloys,  compound,  conductance  of,  396  ;  — 
compound,  resistance-temperature  coeffi- 
cient of,  397  ;  —  heterogeneous,  393 ;  — 
liquid  amalgams,  conductance  of,  397  ;  — 
liquid  conductance  of,  397  ;  —  liquid, 
conductance  of  mixtures  of  sodium  and 
potassium,  398;  —  mixed  crystals,  393; 
—  mixed  crystals,  conductance  change 
with  composition,  394 ;  —  mixed  crys- 
tals, conductance-temperature  coefficient, 
395 ;  —  properties  of,  393 ;  —  thermal 
conductance  of,  403 

Ammonia,  conductance  of  AgCN  in,  53  ;  — 
conductance  of  Hg(CN)2  in,  53;  —  con- 
ductance of  higher  types  of  salts  in, 
105,  108 ;  —  conductance  of  KNO3  in, 
52  ;  —  conductance  of  solutions  in — at 
different  temperatures,  145  ;  —  hydrolytic 
equilibria  in,  230 ;  —  molecular  weight 
in — solutions,  240 ;  —  reactions  in,  see 
Reactions  ;  —  solutions  of  metallic  com- 
pounds in,  215 ;  —  solutions  of  metals 
in,  367;  —  viscosity  of,  65 

Ammonium  Complex,  nature  of  the,  213 
Anions,     complex,     213 ;     —     complex,     in 
liquid  ammonia,  215  ;  —  complex,  nature 
of.    214 

Antimony,  complex  anion  of,  216 

Bases,  organic,  free  radicals  of,  213  ;  —  or- 

§anic,    nature    of    the    positive    ions    of, 
13  ;  —  organic,  positive  ions  of,  212 
Basic  amides,  nature  of,  316 
Bromine,  conductance  of  solutions  in,  50 

Catalytic  action  of  acids,  esterification  con- 
stants in  methyl  alcohol,  289  :  —  action 
of  alcoholate  ion,  291  :  —  action  of  elec- 
trolytes, Arrhenius'  theory  of,  291 ;  — • 
action  of  hydrogen  ion,  velocity  constants. 
690  ;  —  action  of  ions,  287  ;  —  action  of 
ions,  as  influenced  by  their  thermody- 
namic  potential.  291  ;  —  action  of  ions, 
inversion  coefficients,  288 ;  —  action  of 
un-ionized  molecules.  288  ;  —  action,  re- 
lative— of  ions  and  un-ionized  molecules. 
290 


409 


Clausius,   ionization   according  to,   34 
Complexes,  formation  of — in  mixed  solvents, 

177 

Compounds,    metallic,    nature    of,    216 
Concentration   cells,   electromotive  force  of, 

298  ;  —  cells,  energy  effects  in,  306 
Conductance,    abnormal — of    hydrogen    and 

hydroxyl   ions,   205  ;   —  dependence    of — 

on  fluidity  at  different  temperatures,  122  ; 

—  equation,    constants   of,    for    different 
solvents,    75 ;   —  equation,   constants   of, 
for    dilute    aqueous    solutions,    100 ;    — 
equation,  constants  of,  for  solvents  of  low 
dielectric  constant,  77  ;  —  equation,  con- 
stants of,  in  ammonia,  73,  77  ;  —  equa- 
tion, geometrical  interpretation  of,  80  ;  — 
equivalent,  and  transference  numbers,  32  ; 
— equivalent,  defined,   27  ;  —  equivalent, 
influence    of    concentration    on,    30 ;    — 
equivalent,    influence    of    temperature    on 
— in  sulphur  dioxide,  155  ;  —  equivalent, 
influence    of    viscosity    on    limiting    value 
of,  109  ;  —  equivalent,  ionic,  37  ;  —  equi- 
valent,   limiting    value    of,    30 ;    —   equi- 
valent,    limiting    value    of,     in     acetone, 
62  ;   — •   equivalent,   limiting  value   of,   in 
alcoholic  solutions  containing  water,  181 ; 

—  equivalent,  limiting  value  of,  in  differ- 
ent solvents,  62;  —  equivalent,   limiting 
value  of,  for  organic  electrolytes  in  am- 
monia,  60  ;  —  equivalent,  limiting  value 
of,    for   salts   in    ammonia.   59 ;   —   equi- 
valent, of  aqueous  salt  solutions  at  high 
temperatures,     147 ;     —     equivalent,     of 
higher  types  of  salts  at  higher  tempera- 
tures in  water,  148  ;  —  equivalent,  table 
of,    28;    —    function,    applicability    of — 
to   ammonia    solutions,    70 ;    —   function, 
form    of,    67 ;    —    function,    form    of,    in 
dilute  aqueous  solutions,  98  ;  —  function, 
graphical  treatment  of,  69  ;  —  function, 
Kraus     and     Bray's,     68 ;     —     function. 
Storch's,   67  ;  —  in   critical  region,  167  ; 

—  in   critical   region,   in   methyl   alcohol, 
169  ;  —  in  mixed  solvents,   176,  190 ;  — 
in    vapors    near    critical    point,    170 ;    — 
influence    of    complex    formation    on — in 
mixed  solvents,  197  ;  —  influence  of  con- 
centration on,  46  ;  —  influence  of  density 
of  solvent  on,  172  ;  —  influence  of  tem- 
perature   on    --   at   high    concentrations, 
166  ;  —  influence   of  water   on — in   non- 
aqueous  solvents,  178,  179  ;  — influence  of 
water  on — in  solutions  of  acids  in   alco- 
hols, 180  ;  —  ionic,  abnormal  values  of, 
206  ;  —  ionic,  comparison  of,  in  ammonia 
and  water,   64  ;  —  ionic,   comparison  of, 
in  different  solvents,  63  ;   —  ionic,  influ- 
ence  of   temperature   on,    123 ;    —   ionic, 
influence   of  viscosity   on,   111 ;   —  ionic, 
table  of  values  of,   in   ammonia,   64  ;  — 
ionic,  values  of,  in  formic  acid,  207 ;  — 
ionic,  values  of.  in  water.  37  ;  —  of  fused 
salts,  353  ;  —  of  glass,  356  ;  —  of  pure 
substances,    351  ;  —  of    solid    electrolytes, 
359  ;  —  of  solutions  in  non-aqueous  sol- 
vents,     46  ;  —  -temperature     coefficient, 
influence  of  concentration  on  the,  161 ;  — 
-temperature    coefficient    of    solutions    In 
halogen     acids    at    high     concentrations, 
165 

Conduction  process,  relation  between  metal- 
lic  and   electrolytic,  366 


410 


SUBJECT  INDEX 


Conductors,  electrolytic,  14 ;  —  metallic, 
14  384 ;  —  metallic,  anisotropic,  402 ; 
— .  metallic,  influence  of  treatment  on 
properties  of,  402  ;  —  metallic,  influence 
of  pressure  on,  402;  —  metallic,  photo- 
electric properties  of,  402  ;  —  mixed  me- 
tallic and  electrolytic,  366  ;  —  variable, 
399 

Constant,  ionization,  influence  of  water  on 
— of  acids  in  alcohols,  185 

Critical  point,  conductance  in  neighbor- 
hood of,  167 

Density  coefficient  of  ions,  additive  nature 
of  286  •  —  coefficient  of  un-ionized  mole- 
cules, 285 ;  —  of  electrolytic  solutions, 
283  •  —  of  electrolytic  solutions,  as  a 
function  of  ionization,  284;  —  of  elec- 
trolytic solutions,  according  to  Heydweil- 
ler,  284 ;  —  of  solutions  in  acetone,  287  ; 
—  of  solutions  in  ethyl  alcohol,  287  ;  — 
of  solutions  in  methyl  alcohol,  287 

Dielectric  constant,  dependence  of  ioniza- 
tion on,  89  ;  —  constant,  influence  of,  on 
conductance,  16 ;  —  constant,  influence 
of,  on  constants  of  conductance  equation, 
90  ;  —  constant,  influence  of,  on  ioniza- 
tion according  to  Walden,  92 ;  —  con- 
stant, influence  of  salts  on,  92. 

Diffusion  coefficient  of  electrolytes,  280  ;  — 
coefficient  of  electrolytes,  in  presence  of 
other  electrolytes,  282 ;  —  of  electrolytes, 
280 ;  —  of  electrolytes,  in  presence  of 
other  electrolytes,  281 

Dilution  law,  see  Conductance  function 


Electricity  and  matter,  17 ;  —  discrete 
structure  of,  20 

Electrolytes,  conductance  of,  in  pure  state, 
15  ;  —  diffusion  of,  280  ;  —  equilibria  in 
mixtures  of,  218 ;  —  ionization  of,  34  ; 
— •  molecular  weight  of,  in  solution,  37  ; 
—  principles  applicable  to  mixtures  of, 
220 

Electromotive  force  and  conductance  meas- 
urements compared,  300 ;  —  force  of 
concentration  cells,  297,  298 ;  —  force 
of  concentration  cells,  numerical  values, 
300  ;  —  force  of  concentration  cells,  the- 
ory of,  297  ;  —  force  of  concentration 
cells,  with  mixed  electrolytes,  302 

Energy  effects  in  concentration  cells  with 
mixed  electrolytes,  307 

Equilibria,  heterogeneous,  232;  —  homo- 
geneous ionic,  218  ;  —  hydrolytic,  225  ;  — 
hydrolytic,  equations  of,  225  ;  —  in  mix- 
tures with  common  ion,  219 

Ethyl  alcohol,  conductance  of  CoCl2  in — 
at  different  temperatures,  162 

Ethylamine,  conductance  of  solutions  in, 
51  ;  —  conductance  of  solutions  in,  at 
different  temperatures,  159 


Faraday's  Laws,  19  ;  —  Laws,  applicability 
of,  19;  —  Laws,  applicability  of,  to 
metal-ammonia  solutions,  20 ;  —  Laws, 
exceptions  to,  20 

Fluidity,  see  also  Viscosity ;  —  of  mixed 
solvents,  187 

Formates,  conductance  of — compared  with 
acetates  in  water,  102  ;  —  solutions  of, 
in  formic  acid,  101 

Freezing  point,  comparison  of — for  solu- 
tions of  different  salts  in  water,  232 

Fused  salts,  applicability  of  Faraday's  Law 
to,  353  ;  —  salts,  conductance  and  fluid- 
ity compared,  354  ;  —  salts,  conductance 
or,  353 ;  —  salts,  conductance  of  mix- 
tures of,  355  ;  —  salts,  influence  of  tem- 
perature on  conductance  of,  354 


Gases,    conduction   in,   13 

Glass,  conductance  of,  356  ;  —  influence  of 
temperature  on  conductance  of,  357  ;  — 
ionization  value  for,  358 ;  —  speed  of 
ions  in,  359  ;  —  transference  in,  357 

Graphite,    pure,    conductance   of,    400 

Hall  effect,  theory  of,  407 

Heat  effects  in  concentration  cells,  306; 
—  of  dilution  of  electrolytes,  305  ;  —  of 
neutralization  of  acids  and  bases,  304  ;  — 
of  neutralization  of  acids  and  bases  and 
ionization  constant  of  water,  304 

Hexane,    conductance    in,    13,    351 

Hittorf's  numbers,  see  Transference 

Hydration,  from  transference  measurements, 
198 ;  —  influence  of  concentration  on, 
201 ;  —  influence  of — on  conductance, 
201 ;  —  influence  of  temperature  on  125  • 
— •  of  ions  in  water,  198,  200  ;  —  rela- 
tive— of  ions,  201 

Hydrogen  bromide,  conductance  of  methyl 
alcohol  in,  49  ;  —  solubility  of — in  pres- 
ence of  electrolytes,  245 

Hydrolysis,  see  also  Equilibria  ;  —  225  ;  — 
at  low  concentrations  in  water,  228  ;  — 
in  phenol,  244  ;  —  influence  of,  on  con- 
ductance, 228  ;  —  of  salts  at  high  tem- 
peratures, 150 

Insulators,   conductance  of,  351 

Iodine,  conductance  of,  in  sulphur  dioxide, 
322 

Ion,  chloride,  conductance  of,  in  formic 
acid,  207 ;  —  complex  iodide,  214 ;  — 
complex  sulphide,  214 ;  —  conductance, 
independence  of  nature  of  other  ions, 
309  ;  —  conductance,  of  chloride  ion  with 
different  cations  compared,  309  ;  —  con- 
ductance, of  potassium  ion  of  different 
salts  compared,  310  ;  —  hydrogen,  as  ox- 
onium  complex,  205 ;  —  hydrogen,  con- 
ductance of,  in  formic  acid,  207  ;  —  hy- 
drogen, in  liquid  ammonia,  206  •  — - 
hydrogen,  nature  of,  205 ;  —  hydroxyl, 
205 ;  —  product,  constancy  of — for 
strong  electrolytes,  262;  —  pyridonium, 
conductance  of,  in  pyridine,  208 

Ionic  speed,  influence  of  temperature  on, 
124  ;  —  speed,  influence  of  viscosity  on, 
in  differetft  solvents,  111 

Ionization  as  a  result  of  compound  forma- 
tion, 322 ;  —  as  measured  by  conduct- 
ance, 34 ;  —  as  related  to  constitution 
of  electrolyte,  320;  —  constant  of  am- 
monia and  acetic  acid  at  elevated  tem- 
peratures, 149 ;  —  constant  of  water, 
225  ;  —  constant  of  water  and  heat  of 
neutralization,  304  ;  —  constant  of  water 
at  high  temperature,  150 ;  —  dependence 
of,  on  dielectric  constant  according  to 
Walden,  92 ;  —  dependence  of,  on  prop- 
erties of  solvent,  88;  —  dependence  of, 
on  solvent,  48  ;  —  derived  from  osmotic 
and  conductance  measurements  com- 
pared, 233;  —  factors  influencing,  318; 

—  influence  of  temperature  on — in  water, 
150  ;  —  of  electrolytes,  by  freezing  point 
method,  38  ;  —  of  salts  of  organic  bases, 
321 ;  —  values,  table  of.  35 

Ionizing  power  as  dependent  on  dielectric 
constant,  318 ;  —  power  of  solvents  in 
critical  region,  319  ;  —  power  of  solvent 
in  relation  to  constitution,  318 

Ions,  catalytic  action  of,  287  ;  —  charge  on 

—  as  determined  by  conditions,  322  ;  — 
complex  negative,  216  ;  —  complexity  of 
— as  influenced  by  temperature,  125  ;  — 
dimensions  of — as  calculated  by  Born  and 
Lorenz.    202 ;    —   dimensions    of — as    de- 
rived from   conductance,   202 ;    —  hydra- 
tion  of,  in  water  ;  see  Hydration,  198  ;  — 
interaction  of,  with  polar  molecules,  198 ; 


SUBJECT  INDEX 


411 


—  intermediate,    217 ;    —   intermediate, 
influence  of,  on  conductance,  104  ;  —  in- 
termediate, influence  of,  on  dilution  func- 
tion, 97  ;  —  intermediate,  influence  of,  on 
molecular   weight,   41  ;   —  nature   of — in 
electrolytic  solutions,  198 

Isohydric  principle,  219  ;  —  principle,  ap- 
plied to  solubility  data,  262 ;  —  principle, 
test  of,  224 

Law  of  Kohlrausch,  33 ;  —  of  mass  action, 
applicability  of,  to  ammonia  solutions,  56  ; 

—  of   mass   action,    applicability    of,    to 
aqueous   solutions   at   high    temperatures, 
153  ;  —  of  mass  action,  applicability  of, 
to   dilute    aqueous    solutions,    98 ;    —    of 
mass    action,    applicability    of,    to    elec- 
trolytes,   41 ;    —   of   mass   action,    appli- 
cability of,  to  non-aqueous  solutions,  53 ; 

—  of    mass    action,    applicability    of,    to 
solutions  in  formic  acid,  101 ;  —  of  mass 
action,    applicability    of,    to    weak    elec- 
trolytes,  43 ;   —   of   mass   action,   devia- 
tions  from,   in   ammonia,    58,   86 ;   —  of 
mass  action,  graphical  treatment  of,  54  ; 

—  of   mass  action,    limited   applicability 
of,   238 ;   —  of  mass  action,   theories   of 
deviations    from,    96 

Lead,  complex  anion  of,  216 

Lithium   hydride,   conductance  of,    364 ;  — 

hvdride,  nature  of  conduction  process  in, 

365 

Mass-action  constant,  dependence  of,  on  di- 
electric constant,  90  ;  —  constant,  table 
of  values  of — for  different  solvents,  62  ; 

—  constant,   table  of  values  of — for  or- 
ganic   electrolytes    in    ammonia,    60 ;    — 
constant,  table  of  values  of — for  salts  in 
ammonia,  59  ;  —  constant,   table  of  val- 
ues   of — in    acetone,     62 ;    —     function, 
form  of,  for  salts  of  higher  types  in  am- 
monia, 108  ;  —  function,  in  ammonia  and 


water  compared,  55 


function,  in  am- 


monia solutions,  KNO8,  55  ;  —  function, 
influence  of  temperature  on,  153,  156  ;  — 
function,  for  aqueous  KC1  solutions,  45  ; 

—  function     for     HC1     in     water,     45  ; 

—  function,  variation  of,  for  higher  type 
salts  in  water,  106,  107;  —  law  of,  see 
Law 

Metal-ammonia  solutions,  ammoniation  of 
negative  electron  in,  374 :  —  solutions, 
atomic  conductance  of  concentrated  solu- 
tions, 380 ;  —  solutions,  complexes 
formed  in,  367 ;  —  solutions,  conduct- 
ance of  sodium  in,  376  ;  —  solutions,  equi- 
libria in,  371  ;  —  solutions,  limiting  con- 
ductance of  negative  electron  in,  377  ;  — 
solutions,  method  of  determining  rela- 
tive speed  of  ions  in,  372  ;  —  solutions, 
molecular  weight  determinations,  367  ;  — 
solutions,  nature  of  carriers  in,  369  ;  — 
solutions,  properties  of,  366  ;  —  solutions, 
relative  speed  of  ions  in,  numerical  val- 
ues, 373  ;  —  solutions,  specific  conduct- 
ance of  concentrated  solutions  in,  378 ; 

—  solutions,    temperature    coefficient   of. 
382 ;    — •    solutions,    transference    effects 
in,   368 

Methyl  alcohol,  conductance  of  salts  in — 
near  critical  point,  169 

Methylamine,  conductance  of  KI  in.  50  :  — 
conductance  of  KI  in,  at  different  tem- 
peratures, 164  ;  —  conductance  of  solu- 
tions in — at  different  temperatures,  159 

Metallic  alloys,  see  Alloys ;  —  conduction, 
theories  of.  407 

Metals,  see  also  Alloys ;  —  see  also  Con- 
ductors. Metallic ;  —  see  also  Variable 
Conductors ;  —  atomic  conductance  of, 
387  ;  —  change  of  resistance  of,  due  to 
change  of  state,  389  ;  —  change  of  spe- 


cific resistance  of — on  melting,  388 ;  — 
compound,  384 ;  —  conduction  of  solu- 
tions of — in  ammonia,  20 ;  —  conduc- 
tion process  in,  385  ;  —  effects  in — under 
acceleration,  386 ;  —  elementary,  resist- 
ance-temperature coefficient  of,  387,  391  ; 

—  elementary,  resistance-temperature  co- 
efficient of,  at  constant  volume,  393  ;  — 
elementary,    resistance-temperature    coeffi- 
cient of,  in  liquid  state,  392  ;  —  galvano- 
magnetic  properties  of,  405  ;  —  Hall  ef- 
fect  in,   406 ;    —   influence  of  impurities 
on  conductance  of,   400 ;   —  influence   of 
temperature  on   conductance  of,  389  ;  — 
influence  of  temperature   on   conductance 
of,  at  low  temperatures,  389  ;  —  nature 
of,  384  ;  —  optical  properties  of,  407  ;  — 
properties   of,    384 ;   —  relation    between 
thermal    and    electrical    conductance    of, 
403  ;  —  specific  resistance  of  elementary, 
386  ;  —  state  of,  384  ;  —  supraconducting 
state  of,  390  ;  —  thermal  conductance  of, 
403 ;  —  thermal  conductance  of,  at  low 
temperatures,      403 ;     —     thermoelectric 
properties    in,    404 ;    —    thermomagnetic 
properties  in,  405  ;  —  transference  effects 
in,    385 

Mercury  methyl,  properties  of,  213 

Mixed    solvents,    conductance    in,    120;    — 

solvents,  fluidity  of,  187 
Mixtures  of  electrolytes,  equilibria  in,  218  ; 

—  of  electrolytes,  freezing  points  of,  234 
Molecular     weight,     determination     of,     by 

vapor  pressure  method,  238 ;  —  weight, 
from  osmotic  data,  232 ;  —  weight  in 
non-aqueous  solutions,  239 ;  —  weight 
in  sulphur  dioxide,  239 ;  —  weight  of 
electrolytes  by  freezing  point  method,  38  ; 

—  weight  of  electrolytes  in  solution,  37  ; 

—  weight  of   electrolytes  in   water.   232 ; 

—  weight   of   electrolytes,    limitation    of 
method  of  determining,  by  osmotic  meth- 
ods, 40 

Optical  properties  of  electrolytes,  absorp- 
tion coefficients  in  water  and  methyl  alco- 
hol, 295 ;  —  properties  of  electrolytes, 
absorption  curves,  294  ;  —  properties  of 
electrolytes,  extinction  coefficients  of 
acetyloxindon  salts  in  alcohol,  297 ;  — 
properties  of  electrolytes,  extinction  co- 
efficients of  acetyloxindon  salts  in  water, 
296  ;  —  properties  of  electrolytes,  extinc- 
tion coefficients  of  the  chromate  ion,  293  ; 

—  properties    of    electrolytic    solutions, 
292 

Potassium  iodide,  correction  of  conduct- 
ance of,  for  viscosity,  116 

Pressure,  influence  of,  on  conductance,  129, 
134  ;  —  influence  of,  on  conductance,  at 
different  concentrations,  134  ;  —  influence 
of,  on  conductance,  due  to  viscosity 
change  in  non-aqueous  solution,  142 ;  — 
influence  of,  on  conductance,  in  non-aque- 
ous solvents,  139  ;  —  influence  of,  on  con- 
ductance, of  alcohol  solutions,  139 ;  — 
influence  of,  on  conductance,  of  different 
electrolytes,  131 ;  —  influence  of,  on  con- 
ductance of  KC1  in  water,  129 ;  —  in- 
fluence of.  on  conductance,  of  weak  elec- 
trolytes. 136  ;  —  influence  of,  on  electro- 
lytic conduction,  126ffi — influence  of,  on 
viscosity  of  solvent,  126  ;  —  influence  of, 
on  viscosity  of  solutions,  127 

Propyl  alcohol,  influence  of  water  on  con- 
ductance of  solutions  in,  178 

Reactions,  electrolytic,  16;  —  electroly- 
tic, in  ammonia.  314  ;  —  in  ammonia  and 
water,  compared,  314 ;  —  in  electrolytic 
solutions,  312  ;  —  in  solvents  of  low  di- 
electric constant,  317 


412 


SUBJECT  INDEX 


Salts,  conductance  of  higher  types  of,  104  ; 
— •  complex  metal-ammonia,  209  ;  —  com- 
plex metal-ammonia,  conductance  of,  211  ; 
—  complex  metal-ammonia,  ionization  of, 
211  ;  —  complex  metal-ammonia,  Werner's 
theory  of,  210  ;  —  fused,  see  Fused  salts  ; 
— •  of  higher  types,  conductance  of — at 
higher  temperatures  in  water,  148 ;  — 
solid,  applicability  of  Faraday's  Law  to, 
362  ;  —  solid,  change  of  conductance  at 
transition  point,  362  ;  —  solid,  conduct- 
ance of,  359 ;  —  solid,  conductance  of, 
at  different  temperatures,  360  ;  —  solid, 
conductance  of,  lithium  hydride,  see  Li- 
thium hydride,  364 ;  —  solid,  conduct- 
ance of  mixtures  of,  363 ;  —  ternary, 
conductance  of,  in  ammonia,  105,  108  ;  — 
ternary,  variation  of  conductance  func- 
tion for — in  water,  106 
Sodium  acetate,  conductance  of,  in  water, 

102  ;  —  plumbide,  electrolysis  of,  19 
Solubility  experiments,  assumptions  under- 
lying interpretation  of,  264 ;  —  experi- 
ments, constant  concentration  of  un- 
ionized molecules  in,  262 ;  —  Harkins' 
theory  of  influence  of  intermediate  ions 
on,  277  ;  —  influence  of  complex  ions  on, 
267  ;  —  influence  of  electrolyte  on — in 
ethyl  alcohol,  250  ;  —  of  electrolytes  in 
presence  of  common  ion,  254  ;  —  of  elec- 
trolytes in  presence  of  other  electrolytes, 
254  ;  —  of  electrolytes  in  salt  mixtures, 
Bronsted's  theory  of,  337  ;  —  of  gases, 
influence  of  electrolytes  on,  239 ;  —  of 
higher  types  of  salts,  theory  of,  275  ;  — 
of  lithium  carbonate  in  presence  of  non- 
electrolytes,  252 ;  —  of  non-electrolytes 
in  presence  of  electrolytes,  245  ;  —  of 
non-electrolytes,  influence  of  electrolytes 
on  249  ;  —  of  non-electrolytes,  influence 
of  organic  salts  on,  250  ;  —  of  salts  in 
presence  of  non-electrolytes,  251,  253  ;  — 
of  salts  in  presence  of  other  salts,  lan- 
thanum iodate,  274  ;  —  of  salts  in  pres- 
ence of  other  salts,  lead  iodate,  270  ;  — 
of  salts  in  presence  of  other  salts,  silver 
sulphate,  268 ;  —  of  salts  in  presence 
of  other  salts,  strontium  chloride,  271  ; 
—  of  salts  in  salt  mixtures,  ther- 
modynamic  'treatment,  335 ;  —  of  salts 
of  high  type  in  presence  of  other  salts, 
268 ;  —  of  strong  electrolytes  in  pres- 
ence of  other  electrolytes  without  com- 
mon ion,  268 ;  —  of  strong  electrolytes 
in  presence  of  other  strong  electrolytes, 
261  ;  —  of  T1C1  in  presence  of  other  elec- 
trolytes, 261 ;  —  of  weak  acids  in  pres- 
ence of  other  acids,  256 
Solutions,  aqueous,  molecular  weight  in, 
232  ;  —  electrolytic,  15  ;  —  electrolytic, 
conductance  of,  26  ;  —  electrolytic,  den- 
sity of,  283  ;  —  electrolytic,  equilibria  in, 
16 ;  —  electrolytic,  non-aqueous,  46 ;  — 
electrolytic,  optical  properties  of,  292  ;  — 
electrolytic,  reactions  in,  16,  312 ;  — 
electrolytic,  thermal  properties  of,  303 ; 
• — electrolytic,  various  properties  of,  .280; 
— •  non-aqueous,  molecular  weight  in,  239 
Solvents,  mixed,  conductance  in,  176 ;  — 
mixed,  ionization  in,  177  ;  —  pure,  con- 
duction process  in,  352 

Sulphur  dioxide,  conductance  of  KI  in,  47  ; 
— •  dioxide,  conductance  of  solutions  in — 
at  different  temperatures,  155  ;  —  dioxide, 
molecular  weight  of  solutions  in,  239 

Tellurium,  complex  anion  of,  215 
Temperature,  conductance  of  aqueous  solu- 
tions at  elevated,  146 :  —  influence  of, 
on  conductance,  122,  144;  —  influence 
of.  on  conductance  of  ammonia  solutions, 
145  :  —  influence  of,  on  conductance  of 
methylamine  solutions,  146;  —  influence 


of,  on  conductance  of  non-aqueous  solu- 
tions, 154  ;  —  influence  of,  on  conduct- 
ance of  solutions,  51  ;  —  influence  of,  on 
conductance  of  solutions  in  amines,  159  ; 
— •  influence  of,  on  constants  of  con- 
ductance equation,  156 ;  —  influence  of, 
on  ionization  constants,  149  ;  —  influence 
of,  on  ionization  of  salts,  150 

Theories  of  electrolytic  solutions,  miscel- 
laneous, 347  ;  —  relating  to  electrolytic 
solutions,  323 

Theory,  ionic,  17  ;  —  ionic,  origin  of,  21 ;  — 
of  Berzelius,  20  ;  —  of  electrolytic  solu- 
tions, from  thermodynamic  standpoint, 
324  ;  —  of  electrolytic  solutions,  Ghosh's, 
340  ;  —  of  electrolytic  solutions,  Ghosh's, 
compared  with  experiments,  341 ;  — 
of  electrolytic  solutions,  Hertz's,  345 ; 

—  of   electrolytic    solutions,    inconsisten- 
cies in,  328  ;  —  of  electrolytic  solutions, 
Jahn's,  326  ;  —  of  electrolytic  solutions, 
limitations    of — for     strong    electrolytes, 
323 ;   —  of  electrolytic   solutions,   Malm- 
strom's    and    Kjellin's,    339;    —    of    elec- 
trolytic   solutions,    Milner's,    343 ;    —    of 
electrolytic    solutions,    present    state    of, 
summarized,  349  ;  —  of  Grotthuss,  206  ; 

—  of  Werner,  210 

Thermal  properties  of  electrolytic  solutions, 
303 

Thermodynamic  potential  of  'electrolytes 
and  electromotive  force,  298  ;  —  proper- 
ties of  electrolytic  solutions,  328 ;  — 
properties  of  electrolytic  solutions,  nu- 
merical values,  333 

Transference  effects  accompanying  the  cur- 
rent, 21  ;  —  numbers,  by  moving  bound- 
ary method,  23  ;  —  numbers,  change  of, 
at  low  concentrations,  307  ;  —  numbers, 
change  of,  for  strong  acids,  307  ;  —  num- 
bers, definition  of,  21  ;  —  numbers,  in 
ammonia,  64 ; —  numbers,  influence  of 
complex  ions  on,  24  ;  —  numbers,  influ- 
ence of  concentration  on,  24  ;  —  numbers, 
influence  of  hydration  on,  22,  198 ;  — 
numbers,  influence  of  temperature  on,  26  ; 

—  numbers,  methods  of  determining.  22  ; 
— •   numbers,    table   of,   25  ;    —   numbers, 
true,  200 ;  —  numbers,   true,  relation  of 
— to   ordinary,    199 

Van't  Hoff's  factor,  38;  —  factor,  limiting 
value  of,  41 

Variable  conductors,  change  of  conductance 
at  transition  points,  401  ;  —  conductors, 
specific  conductance  of,  400 ;  —  conduc- 
tors, thermal  conductance  of,  403 

Velocity  of  reactions  as  influenced  by  ions, 
287 

Viscosity  change  due  to  salts  in  different 
solvents,  112  ;  —  change,  influence  of  — 
due  to  non-electrolytes,  on  conductance, 
119,  121  :  —  dependence  of — on  dielec- 
tric constant,  112 ;  —  effect,  correction 
of  conductance  for.  114  ;  —  effect,  nega- 
tive. 113 ;  —  influence  of  concentration 
on,  112  ;  — influence  of  on  conductance, 
111  ;  —  influence  of,  on  conductance  in 
mixed  solvents,  176 ;  —  influence  of  on 
conductance  in  non-aqueous  solutions, 
118  ;  —  influence  of,  on  conductance  of 
concentrated  solutions.  116;  —  influence 
of  on  conductance  of  different  ions,  114  ; 
— influence  of,  on  ionic  speeds  in  different 
solvents.  Ill ;  —  influence  of,  on  A0 
values.  109 ;  —  influence  of  pressure  on 
— in  different  solvents,  143  ;  —  influence 
of  temperature  on.  113  ;  —  of  ammonia 
at  boiling  point,  65:  —  of  fused  salts, 
354  ;  —  of  mixed  solvents,  177 

Water,  influence  of — on  conductance  of 
acids  in  alcohols.  180,  186 ;  —  ioniza- 
tion constant  of,  225 


NAME  INDEX 


Acree,  291 ;  —  see  Loomis ;  —  see  Robert- 
son 

Adams,  233,  234,  343  ;  —  and  Lanman,  see 
Lewis 

Akerlof,  292 

Allmand  and  Polack,  300,  334 

Amagat,    130 

Andrews,  see  Kendall 

Archibald,  49,  165,  205  ;  —  and  Mclntosh, 
see  Steele 

Argo,  see  Gibson 

Arrhenius,  17,  18,  21,  34,  37,  38,  42,  54,  219, 

221.  225,  267,  280,  281,  287,  291 
Avogadro,  341 

Baedeker,   385 

Baldwin,  see  Cady 

Bancroft,   68 

Bates,  69  ;  —  and  Vinal,  19 

Beattie,    see   Maclnnes 

Bedford,    233 

Bekier,  see  Bruner 

Benedicks,    388 

Benrath    and   Wainoff,   364 

Berzelius,    20,    21 

Biltz,   249,    367 

Bingham   and  McMaster,   see  Jones 

Bishop,   see  Kraus 

Bisson.   see   Randall 

Bjerrum.  331.  337 

Blanchard,   119 

Born.    202.   203,   204 

Bottger,    228 

Bousfield  and  Lowry,  114 

Braun,    249 

Braune,    185 

Bray,  68.  266  ;  —  see  Kraus ;  —  and  Hunt, 

222,  267  ;  —  and  MacKay,  214  ;  —  and 
Winninghoff,  261,  262,  265 

Bridgman,    390 

Brighton  and   Sebastian,  see  Lewis 

Bronsted.  331.  333,  337.  338,  339 

Bruner   and   Bekier,   322;   —   and   Galecki, 

322 

Bruyn,  Lobry  de,  198 
Buchbock,    198 
Bunting,  see  Schlesinger 

Cad.v,    367,   373 ;    —  see   Franklin,  —   and 
Baldwin,  317  ;  —  and  Lichtenwalter,  317 
Caldwell.  see  Hantzsch 
Callis,    321.    353;    --   and    Greer,    318 
Calvert,    see    Schlesinger 
Carlisle,  see  Nicholson 
Cavanagh,  343 
Centnerszwer.  see  Walden 
Chapman  and  George,  340 
Chiu.  215 
Chow,  303 
Clark.    121 
Clausius,   34 
Clay,    389.    400,   406 
Coehn,  213 

Cohen.   126.  127.  131,   134,   138 
Coleman,    see   McBain ;    —   see    Schlesinger 
Crommelin,  389 
Cushman.  see  Randall 

Dalton.  326 

Danneel.    206 

Darby.  49.  79.  357.  358 

Davis   and  Jones,   113 


413 


Davy,  Sir  Humphrey,  19 

Dawson  and  Powis,  290 

de    Bruyn,    Lobry,    198 

Dennison  and  Steele,  310,  311 

de   Szyszkowski,   69 

Dewar  and  Fleming,  400 

Drude,  407  ;  —  and  Nernst,  284 

Dummer,  204 

Dutoit  and  Rappeport,  47  ;  —  and  Levrier, 

Eastman,    see    Noyes 

Eggert,  see  Tubandt 

Einstein,     202,    204 

Ellis,  300,  306,  307  ;  —  see  Noyes 

Essex  and  Meacham,  see  Loomis 

Euler,    248,    249 

Eversheim,  319 

Falk,    see   Noyes 

Fanjung,   136 

Faraday,  14,  17,  19,  20,  21,  33,  206,  353, 
357,  362,  363 

Fenninger,  397 

Ferguson,  see  Tolman 

Fitzgerald,   50,  51,   109,   112,   119,   158,   163 

Fleming,  see  Dewar 

Foote  and  Martin,   353 

Forbes,  268 

Franklin,  47,  52,  69,  108,  155.  161,  206,  207, 
230,  315,  316.  373  ;  —  and  Cady.  64  ;  — 
and  Kraus,  52,  53,  55,  105,  145,  206, 
240,  316  ;  —  and  Stafford,  206,  316 

Franz,  see  Wiedemann 

Frazer  and  Sease,  see  Lovelace 

Galecki.  see  Bruner 

Gates,  317,  318 

Geffcken,  245 

George,  see  Chapman 

Georgievics.  324,  348 

Ghosh,  324,  340,  341,  342,  343 

Gibbs.   325.   326 

Gibson  and  Argo,   367 

Goldschmidt.   180.  182.  183  ;  —  and  Thue- 

sen,  181,  183.  184,  289 
Goodwin   and  Mailey,   353,   355 
Gordon,   249 
Graetz,    407 
Green,  121 
Greer,  see  Callis 
Gross,   see  Kendall 
Grotthuss,    206 
Guertler,  393 

Hall,  386.  406,  407:  —  and  Harkins,  233. 

234.  235 
Hantzsch.  293,  295,  296;  —  and  Caldwell, 

206,    208 
Harkins.   41.    269.    275.   277;   —  see  Hall; 

—  and  Pearce,  273 
Harned,   291,  292,  300,   303,   306,   307,  331, 

335 

Hartung,  242 
Heberlein,    see  Kiister 
Helmholtz.    17.    20 
Herty,    see    Werner 
FTprtz.  345.  346,  347 
Heuse.    239 
Heydweiller,    283,    284,    285,    286;    —    see 

Kohlrausch  ;  —  and  Kopfermann,  358 


414 


NAME  INDEX 


Hine,  397 

Hittorf,  21,  22,  23,  24,  34,  206,  345,  348 

Hof,  see  Onnes 

Holborn,    see    Kohlrausch 

Hoist,  see  Onnes 

Hugot,  "215 

Hunt,  see  Bray 

Jaeger    and    Kapma,    355 

Jaffa1,   351 

Jahn,  326,  327,  328 

Johnston,   110,   114,   122 

Jones,  see  Davis ;  —  and  Veazey,  187,  190  ; 

—  Bingham  and  McMaster,  187,  190,  191, 

192,  194 

Kalian,  183 

Kahlenberg,  317 

Kanolt,  225  ;  —  see  Morgan 

Kato,  see  Noyes 

Kendall,  43,  256,  263,  267  ;  —  and  Andrews, 
260  ;  —  and  Gross,  321 

Kerschbaum,  see  LeBlanc 

Keyes  and  Winninghoff,  74 

Kjellin,   339 

Koenigsberger,  385,  397,  398,  402,  404.  408 

Kohlrausch,  33,  34,  110,  224  ;  —  and  Heyd- 
weiller,  225,  352;  —  and  Holborn,  27 

Kohnstamm,    see   Van   der    Waals 

Kopfermann,  see   Heydweiller 

Korber,    129.   131,   134 

Kraus,  20,  44.  68.  84,  98,  100,  111,  116, 
123,  146,  168,  172,  213.  216.  322,  340, 
343.  367,  376,  381,  382,  384.  393  ;  —  and 
Bishop,  178  ;  —  and  Bray,  52,  56,  58,  60, 
61,  64,  68,  70,  72,  74,  77,  82.  98,  109, 
208 ;  —  and  Lucasse,  378,  381 ;  —  see 
Franklin 

Kurtz,  74,  243 

Kiister,  214 ;  —  and  Heberlein,  214 

Lanman  and  Adams,  see  Lewis 

Lattey,  92 

LeBlanc  and  Kerschbaum,  357 

Levrier,   see  Dutoit 

Lewis,  23.  308,  331 ;  —  Adams  and  Lan- 
man, 385 ;  —  Brighton  and  Sebastian, 
300 ;  —  and  Randall,  330,  332,  333,  335, 
337,  345 

Lichtenwalter,  see  Cady 

Linhart,  300 

Lodge,   23 

Loomis  and  Acree,  300;  —  Essex  and 
Meacham,  300 

Lorenz,  202,  203,  204,  347,  356,  403  ;  —  see 
'Fubandt 

Lovelace.    Frazer   and   Sease,    238 

Lowenherz,  225 

Lownds,    402 

Lowry,  see  Bousfleld 

Lucasse,  206,  380,  383 ;  —  see  Kraus 

McBain  and   Coleman.   242 

McCoy  and  Moore,  213,  384 ;  —  and  West, 

398 

MacDougall,   68 
MacKay,  see  Bray 
Maclnnes,  308,  309  ;  —  see  Washburn  ;  — 

and  Beattie,  300  ;  —  and  Parker,  301 
Mclntoah  and  Archibald,  see  Steele 
McLauchlan,  249 

McMaster  and  Bingham,  see  Jones 
Magie,   283 
Mailey.  see  Goodwin 
Malmstrom,   339 

Martin,   see  Foote ;  —  see  Schlesinger 
Meacham  and  Essex,  see  Loomis 
Melcher,    see   Noyes 
Millard,  307  ;  —  see  Washburn 
Milner,     337,     343,    344,     347 
Moers,     364 
Moissan,  319 
Moo.re,  see  McCoy 


Morgan  and  Kanolt,  198 
MulJinix,  see  Schlesinger 

Nernst,  89,  225,  238,  245,  280,  299,  302, 
326,  328,  339,  401 ;  —  see  Drude 

Nicholson  and  Carlisle,   19 

Noyes,  146,  148,  149,  150,  152,  267,  304, 
308,  340  ;  —  and  Eastman,  41,  148  ;  — 
and  Ellis,  300  ;  —  and  Falk,  24,  26,  30, 
35,  37,  38,  114,  232,  309,  310,  337  ;  —  and 
Kato,  308 ;  —  and  Melcher,  228 ;  and 
Sammet,  308 

Ohm,  22,   352 
5holm,   121,   204,  280 

Onnes,    Kammerlingh,    389,    406 ;    —    and 

Hof,  400  ;  —  and  Hoist,  403 
Ostwald,   287,  288,  348 

Ottiker,   208 

Palmaer,  213,  384 

Parker,  see  Maclnnes 

Partington,   340 

Patroni,  see  Poma 

Pearce,  see  Harkins 

Peck,   19,   216 

Peltier,    404 

Planck,   136,   137,  141,   326 

Plotnikow   and    Rokotjan,   79 

Polack,    see    Allmand 

Poma,    302 ;    —   and    Patroni,    302 

Poole,   352 

Powis,  see  Dawson 

Ramstedt,   290 

Randall,  see  Lewis  ;  —  and  Bisson,  305  ;  — 

and    Cushman,   300 
Raoult,    38 
Rappeport,  see  Dutoit 
Reed,   see  Schlesinger 
Reychler,   348 
Richards   and    Stull,   19 
Richarz,  388 
Riesenfeld,   242 

Rimbach  and  Weitzel.  162,  163 
Robertson  and  Acree,  207 
Roemer,   see   Thiel 
Rohrs.   287 

Rokotjan,  see  Plotnikow 
Rontg'en,   127 
Rothmund.  245,  249,  252 
Rupert,    353 
Ruthenberg.  287 
Ryerson,   121 

Sachs,   see  Warburg 

Sack,  145 

Sammet,  see  Noyes 

Sammis,  317 

Schlesinger.  101.  102,  103,  230;  —  and 
Calvert,  101,  208  ;  —  and  Bunting.  101, 
207  ;  —  and  Coleman.  101  :  —  and  Mar- 
tin. 101,  207 ;  —  and  Mullinix,  101 ;  — 
and  Reed,  101 

Schmidt,    139,   141,   142 

Sease  and  Frazer.   see  Lovelace 

Sebastian  and  Brighton,  see  Lewis 

Serkov,   242 

Setschenow,  249 

Smith,  see  Steam  ;  —  Steam  and  Schnei- 
der, 305 

Smyth,  19,  216.  322 

Snethlage,    324 

Somerville.    393,    396 

Sprung.   112 

Stafford,    see  Franklin 

Steele.  see  Dennison :  —  Mclntosh  and 
Archibald,  206.  347 

Steam  and  Schneider,  see  Smith  ;  —  and 
Smith,  305 

Steiner,    249 

Stewart,  see  Tolman 

Stieglitz,    264,    267 


NAME  INDEX  415 

Stokes,  202,  204  Veazey,  see  Jones 

Storch,  67,  68,  69,  98,  348  Vinal,  see  Bates 
Stull,   see  Richards 

Szyszkowski,  de,  69  Wainoff,  gee  Benrath 

Walden,  92,  93,  95,  110,  241,  320,  322  ;  — 

rr               „    100    191     IQ«    IQ?    190  and  Centnerszwer,  146,  239 

Tammann    129,  131,  136,  137,  138  Warburg   and    Sachs,    127;    —  and   Teget- 

layior,    zyu  meier     359 

Tegetmeier    see  Warburg  Washburn.   26.   43,   99,   100,   114,   121.   198, 

Thiel  and  Roemer    230  199    228    239  ;  —  and  Maclnnes,  232  ;  - 

Thomson,    J.    J~   SJO,    406     407  and  Millkrd,  198  ;  —  and  Weiland,  98 

Thomson,  Sir  William,  89,  339,  404  Weiland,  44;  —  see  Washburn 


Goldschmidt  ;         f  312  ;  _  and  Herty, 

Tolman  297  :  —  and  Ferguson,  300  ;  —  and       w^  gee  McCoy 


•&„„*„+    Qfio  .         QT1/,        Wiedemann  and  Franz,  403 
Tuhandt,  dbd  ;  —  ana  Ji,ggert,  dbd  ;  —  ana 


Lorenz,  19,   355,  356,   360,   362,   364  Winkelmann,    385,    407 

Winninghoff,   see  Bray  ;   —  see  Keyes 

Van  dor  Waals,  42.  325,  326  WOrmann,    304 

van    Everdingen,    402 
van't   Hoff,   38,   239,   337,   343  Zeitfuchs,  215 


YC  3261 


M543792 


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